%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.08", %%% date = "04 March 2014", %%% time = "07:57:01 MST", %%% filename = "canjmath2000.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "51040 19687 100307 953165", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, BibTeX, Canadian Journal of %%% Mathematics, Journal canadien de %%% math{\'e}matiques", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of the %%% Canadian Journal of Mathematics = Journal %%% canadien de math{\'e}matiques (CODEN CJMAAB, %%% ISSN 0008-414X (print), 1496-4279 %%% (electronic)), published by the Canadian %%% Mathematical Society = Soci{\'e}t{\'e} %%% canadienne de math{\'e}matiques for the %%% decade 2000--2009. %%% %%% Publication began with Volume 1, Number 1, in %%% 1949. The journal was published quarterly %%% from 1949 to 1964, and since then, appears %%% bimonthly in February, April, June, August, %%% October, and December. %%% %%% Articles may be published in either English %%% or French, and English abstracts are %%% sometimes provided for articles in French. %%% %%% The journal has a World-Wide Web sites at %%% %%% http://cms.math.ca/cjm/ %%% http://math.ca/Journals/ %%% http://cms.math.ca/Publications/CJM-CMB.html %%% http://www.utpjournals.com/cjm/cjm.html %%% http://www.camel.math.ca/CMS/CJM/ %%% %%% Electronic full text of articles is available %%% to qualified subscribers, and for older %%% issues, to anyone. %%% %%% At version 1.08, the COMPLETE year coverage %%% looked like this: %%% %%% 1997 ( 2) 2003 ( 51) 2009 ( 67) %%% 1998 ( 1) 2004 ( 58) 2010 ( 1) %%% 1999 ( 1) 2005 ( 54) 2011 ( 0) %%% 2000 ( 52) 2006 ( 47) 2012 ( 1) %%% 2001 ( 47) 2007 ( 57) %%% 2002 ( 52) 2008 ( 59) %%% %%% Article: 550 %%% %%% Total entries: 550 %%% %%% BibTeX citation tags are uniformly chosen as %%% name:year:abbrev, where name is the family %%% name of the first author or editor, year is a %%% 4-digit number, and abbrev is a 3-letter %%% condensation of important title %%% words. Citation tags are automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted in %%% publication order, using bibsort -byvolume. %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\input canjmath.sty" # "\ifx \undefined \frak \let \germ = \bf \else \let \germ = \frak \fi" # "\ifx \undefined \iindex \def \iindex#1{} \fi" # "\ifx \undefined \Dbar \def \Dbar {\leavevmode\raise0.2ex\hbox{--}\kern-0.5emD} \fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" # "\ifx \undefined \mathbf \def \mathbf #1{{\bf #1}} \fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" # "\ifx \undefined \mathfrak \let \mathfrak = \mathcal \fi" # "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}}\fi" # "\ifx \undefined \refcno \def \refcno{Cno. } \fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-CAN-J-MATH= "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques"} %%% ==================================================================== %%% Bibliography entries: @Article{Edward:1997:STN, author = "Julian Edward", title = "Spectral theory for the {Neumann} {Laplacian} on planar domains with horn-like ends", journal = j-CAN-J-MATH, volume = "49", number = "??", pages = "232--262", month = "????", year = "1997", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-1997-012-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:07 MDT 2011", bibsource = "http://cms.math.ca/cjm/v49/; http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See corrigendum \cite{Edward:2000:CST}.", abstract = "The spectral theory for the Neumann Laplacian on planar domains with symmetric and horn-like ends is studied. For a large class of such domains and it is proven that the Neumann Laplacian has no singular continuous spectrum and that the pure point spectrum consists of eigenvalues of finite multiplicity which can accumulate only at $0$ or $\infty$. The proof uses Mourre theory.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Stahl:1997:ZSG, author = "Saul Stahl", title = "On the zeros of some genus polynomials", journal = j-CAN-J-MATH, volume = "49", number = "??", pages = "617--640", month = "????", year = "1997", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-1997-029-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:07 MDT 2011", bibsource = "http://cms.math.ca/cjm/v49/; http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See erratum \cite{Stahl:2008:EZS}.", abstract = "In the genus polynomial of the graph $G$ and the coefficient of $x^k$ is the number of distinct embeddings of the graph $G$ on the oriented surface of genus $k$. It is shown that for several infinite families of graphs all the zeros of the genus polynomial are real and negative. This implies that their coefficients and which constitute the genus distribution of the graph and are log concave and therefore also unimodal. The geometric distribution of the zeros of some of these polynomials is also investigated and some new genus polynomials are presented.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Froese:1998:UBR, author = "Richard Froese", title = "Upper bounds for the resonance counting function of {Schr{\"o}dinger} operators in odd dimensions", journal = j-CAN-J-MATH, volume = "50", number = "??", pages = "538--546", month = "????", year = "1998", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-1998-029-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:07 MDT 2011", bibsource = "http://cms.math.ca/cjm/v50/; http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See correction \cite{Froese:2001:CUB}.", abstract = "The purpose of this note is to provide a simple proof of the sharp polynomial upper bound for the resonance counting function of a Schr{\"o}dinger operator in odd dimensions. At the same time we generalize the result to the class of super-exponentially decreasing potentials.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{vanderPoorten:1999:VDE, author = "Alfred van der Poorten and Kenneth S. Williams", title = "Values of the {Dedekind} Eta Function at Quadratic Irrationalities", journal = j-CAN-J-MATH, volume = "51", number = "1", pages = "176--224", month = feb, year = "1999", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-1999-011-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11F20, 11E45", bibdate = "Sat Sep 10 15:39:08 MDT 2011", bibsource = "http://cms.math.ca/cjm/v51/; http://www.math.utah.edu/pub/tex/bib/canjmath1990.bib; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See corrigendum \cite{vanderPoorten:2001:VDE}.", abstract = "Let $d$ be the discriminant of an imaginary quadratic field. Let $a$, $b$, $c$ be integers such that $$ b^2 - 4ac = d, \quad a > 0, \quad \gcd (a,b,c) = 1. $$ The value of $\bigl|\eta \bigl( (b + \sqrt{d})/2a \bigr) \bigr|$ is determined explicitly, where $\eta(z)$ is Dedekind's eta function $$ \eta (z) = e^{\pi iz/12} \prod^\ty_{m=1} (1 - e^{2\pi imz}) \qquad \bigl( \im(z) > 0 \bigr). \eqno({\rm im}(z)>0). $$", acknowledgement = ack-nhfb, ams-subject-primary = "11F20, 11E45", fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", journalabbrev = "CJM", keywords = "binary quadratic forms; Dedekind eta function; form class group; quadratic irrationalities", refnum = "0965", } @Article{Aizenberg:2000:SCS, author = "Lev Aizenberg and Alekos Vidras", title = "On Small Complete Sets of Functions", journal = j-CAN-J-MATH, volume = "52", number = "1", pages = "3--30", month = feb, year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-001-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip $T_{\alpha}\subset {\bf C}^2$. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in ${\bf C}^n$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chan:2000:RTM, author = "Heng Huat Chan and Wen-Chin Liaw", title = "On {Russell}-Type Modular Equations", journal = j-CAN-J-MATH, volume = "52", number = "1", pages = "31--46", month = feb, year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-002-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we revisit Russell-type modular equations, a collection of modular equations first studied systematically by R. Russell in 1887. We give a proof of Russell's main theorem and indicate the relations between such equations and the constructions of Hilbert class fields of imaginary quadratic fields. Motivated by Russell's theorem, we state and prove its cubic analogue which allows us to construct Russell-type modular equations in the theory of signature $3$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chinburg:2000:CTG, author = "T. Chinburg and M. Kolster and V. P. Snaith", title = "Comparison of {$K$}-Theory {Galois} Module Structure Invariants", journal = j-CAN-J-MATH, volume = "52", number = "1", pages = "47--91", month = feb, year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-003-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that two, apparently different, class-group valued Galois module structure invariants associated to the algebraic $K$-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dhersin:2000:SCA, author = "Jean-St{\'e}phane Dhersin and Laurent Serlet", title = "A Stochastic Calculus Approach for the {Brownian} Snake", journal = j-CAN-J-MATH, volume = "52", number = "1", pages = "92--118", month = feb, year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-004-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the ``Brownian snake'' introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that It{\^o}'s formula holds for a wide class of functionals. As a consequence, we give a new proof of the connections between the Brownian snake and super-Brownian motion. We also give a new definition of the Brownian snake as the solution of a well-posed martingale problem. Finally, we construct a modified Brownian snake whose lifetime is driven by a path-dependent stochastic equation. This process gives a representation of some super-processes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Edward:2000:CST, author = "Julian Edward", title = "Corrigendum to {``Spectral Theory for the Neumann Laplacian on Planar Domains with Horn-Like Ends''}", journal = j-CAN-J-MATH, volume = "52", number = "1", pages = "119--122", month = feb, year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-005-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{Edward:1997:STN}.", abstract = "Errors to a previous paper (Canad. J. Math. (2) {\bf 49}(1997), 232--262) are corrected. A non-standard regularisation of the auxiliary operator $A$ appearing in Mourre theory is used.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Harbourne:2000:AFP, author = "Brian Harbourne", title = "An Algorithm for Fat Points on {$\mathbf{P}^2$}", journal = j-CAN-J-MATH, volume = "52", number = "1", pages = "123--140", month = feb, year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-006-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $F$ be a divisor on the blow-up $X$ of $\pr^2$ at $r$ general points $p_1, \dots, p_r$ and let $L$ be the total transform of a line on $\pr^2$. An approach is presented for reducing the computation of the dimension of the cokernel of the natural map $\mu_F \colon \Gamma \bigl( \CO_X(F) \bigr) \otimes \Gamma \bigl( \CO_X(L) \bigr) \to \Gamma \bigl( \CO_X(F) \otimes \CO_X(L) \bigr)$ to the case that $F$ is ample. As an application, a formula for the dimension of the cokernel of $\mu_F$ is obtained when $r = 7$, completely solving the problem of determining the modules in minimal free resolutions of fat point subschemes\break $m_1 p_1 + \cdots + m_7 p_7 \subset \pr^2$. All results hold for an arbitrary algebraically closed ground field $k$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2000:NRA, author = "Chi-Kwong Li and Tin-Yau Tam", title = "Numerical Ranges Arising from Simple {Lie} Algebras", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "141--171", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-007-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A unified formulation is given to various generalizations of the classical numerical range including the $c$-numerical range, congruence numerical range, $q$-numerical range and von Neumann range. Attention is given to those cases having connections with classical simple real Lie algebras. Convexity and inclusion relation involving those generalized numerical ranges are investigated. The underlying geometry is emphasized.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mao:2000:CBC, author = "Zhengyu Mao and Stephen Rallis", title = "Cubic Base Change for {$\GL(2)$}", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "172--196", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-008-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove a relative trace formula that establishes the cubic base change for GL(2). One also gets a classification of the image of base change. The case when the field extension is nonnormal gives an example where a trace formula is used to prove lifting which is not endoscopic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Radjavi:2000:SOS, author = "Heydar Radjavi", title = "Sublinearity and Other Spectral Conditions on a Semigroup", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "197--224", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-009-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Subadditivity, sublinearity, submultiplicativity, and other conditions are considered for spectra of pairs of operators on a Hilbert space. Sublinearity, for example, is a weakening of the well-known property $L$ and means $\sigma(A+\lambda B) \subseteq \sigma(A) + \lambda \sigma(B)$ for all scalars $\lambda$. The effect of these conditions is examined on commutativity, reducibility, and triangularizability of multiplicative semigroups of operators. A sample result is that sublinearity of spectra implies simultaneous triangularizability for a semigroup of compact operators.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Tarrio:2000:LCC, author = "Leovigildo Alonso Tarr{\'\i}o and Ana Jerem{\'\i}as L{\'o}pez and Mar{\'\i}a Jos{\'e} Souto Salorio", title = "Localization in Categories of Complexes and Unbounded Resolutions", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "225--247", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-010-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we show that for a Grothendieck category $\A$ and a complex $E$ in $\CC(\A)$ there is an associated localization endofunctor $\ell$ in $\D(\A)$. This means that $\ell$ is idempotent (in a natural way) and that the objects that go to 0 by $\ell$ are those of the smallest localizing (= triangulated and stable for coproducts) subcategory of $\D(\A)$ that contains $E$. As applications, we construct K-injective resolutions for complexes of objects of $\A$ and derive Brown representability for $\D(\A)$ from the known result for $\D(R\text{-}\mathbf{mod})$, where $R$ is a ring with unit.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Binding:2000:SPN, author = "Paul A. Binding and Patrick J. Browne and Bruce A. Watson", title = "Spectral Problems for Non-Linear {Sturm--Liouville} Equations with Eigenparameter Dependent Boundary Conditions", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "248--264", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-011-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The nonlinear Sturm--Liouville equation -(py')' + qy = \lambda(1 - f)ry \text{ on } [0,1] is considered subject to the boundary conditions (a_j\lambda + b_j) y(j) = (c_j\lambda + d_j) (py') (j), \quad j = 0,1. Here $a_0 = 0 = c_0$ and $p,r > 0$ and $q$ are functions depending on the independent variable $x$ alone, while $f$ depends on $x$, $y$ and $y'$. Results are given on existence and location of sets of $(\lambda,y)$ bifurcating from the linearized eigenvalues, and for which $y$ has prescribed oscillation count, and on completeness of the $y$ in an appropriate sense.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Brion:2000:OCS, author = "Michel Brion and Aloysius G. Helminck", title = "On Orbit Closures of Symmetric Subgroups in Flag Varieties", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "265--292", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-012-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study $K$-orbits in $G/P$ where $G$ is a complex connected reductive group, $P \subseteq G$ is a parabolic subgroup, and $K \subseteq G$ is the fixed point subgroup of an involutive automorphism $\theta$. Generalizing work of Springer, we parametrize the (finite) orbit set $K \setminus G \slash P$ and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of $\theta$-stable (resp. $\theta$-split) parabolic subgroups. We also describe the decomposition of any $(K,P)$-double coset in $G$ into $(K,B)$-double cosets, where $B \subseteq P$ is a Borel subgroup. Finally, for certain $K$-orbit closures $X \subseteq G/B$, and for any homogeneous line bundle $\mathcal{L}$ on $G/B$ having nonzero global sections, we show that the restriction map $\res_X \colon H^0 (G/B, \mathcal{L}) \to H^0 (X, \mathcal{L})$ is surjective and that $H^i (X, \mathcal{L}) = 0$ for $i \geq 1$. Moreover, we describe the $K$-module $H^0 (X, \mathcal{L})$. This gives information on the restriction to $K$ of the simple $G$-module $H^0 (G/B, \mathcal{L})$. Our construction is a geometric analogue of Vogan and Sepanski's approach to extremal $K$-types.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Collin:2000:FHK, author = "Olivier Collin", title = "Floer Homology for Knots and {$\SU(2)$}-Representations for Knot Complements and Cyclic Branched Covers", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "293--305", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-013-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this article, using 3-orbifolds singular along a knot with underlying space a homology sphere $Y^3$, the question of existence of non-trivial and non-abelian $\SU(2)$-representations of the fundamental group of cyclic branched covers of $Y^3$ along a knot is studied. We first use Floer Homology for knots to derive an existence result of non-abelian $\SU(2)$-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian $\SU(2)$-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in $S^3$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cunningham:2000:CDZ, author = "Clifton Cunningham", title = "Characters of Depth-Zero, Supercuspidal Representations of the Rank-$2$ Symplectic Group", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "306--347", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-014-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper expresses the character of certain depth-zero supercuspidal representations of the rank-2 symplectic group as the Fourier transform of a finite linear combination of regular elliptic orbital integrals---an expression which is ideally suited for the study of the stability of those characters. Building on work of F. Murnaghan, our proof involves Lusztig's Generalised Springer Correspondence in a fundamental way, and also makes use of some results on elliptic orbital integrals proved elsewhere by the author using Moy-Prasad filtrations of $p$-adic Lie algebras. Two applications of the main result are considered toward the end of the paper.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Perez:2000:SQO, author = "P. D. Gonz{\'a}lez P{\'e}rez", title = "Singularit{\'e}s quasi-ordinaires toriques et poly{\`e}dre de {Newton} du discriminant. ({French}) [{Quasi-ordinary} toric singularities and {Newton} polyhedron of the discriminant]", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "348--368", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-016-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Nous {\'e}tudions les polyn{\^o}mes $F \in \C \{S_\tau\} [Y] $ {\`a} coefficients dans l'anneau de germes de fonctions holomorphes au point sp{\'e}cial d'une vari{\'e}t{\'e} torique affine. Nous g{\'e}n{\'e}ralisons {\`a} ce cas la param{\'e}trisation classique des singularit{\'e}s quasi-ordinaires. Cela fait intervenir d'une part une g{\'e}n{\'e}ralization de l'algorithme de Newton--Puiseux, et d'autre part une relation entre le poly{\`e}dre de Newton du discriminant de $F$ par rapport {\`a} $Y$ et celui de $F$ au moyen du polytope-fibre de Billera et Sturmfels \cite{Sturmfels}. Cela nous permet enfin de calculer, sous des hypoth{\`e}ses de non d{\'e}g{\'e}n{\'e}rescence, les sommets du poly{\`e}dre de Newton du discriminant a partir de celui de $F$, et les coefficients correspondants {\`a} partir des coefficients des exposants de $F$ qui sont dans les ar{\^e}tes de son poly{\`e}dre de Newton.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Granville:2000:UBL, author = "Andrew Granville and R. A. Mollin and H. C. Williams", title = "An Upper Bound on the Least Inert Prime in a Real Quadratic Field", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "369--380", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-017-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is shown by a combination of analytic and computational techniques that for any positive fundamental discriminant $D > 3705$, there is always at least one prime $p < \sqrt{D}/2$ such that the Kronecker symbol $\left(D/p\right) = -1$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Miyachi:2000:HSE, author = "Akihiko Miyachi", title = "{Hardy} Space Estimate for the Product of Singular Integrals", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "381--411", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-018-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "$H^p$ estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Varopoulos:2000:GPT, author = "N. Th. Varopoulos", title = "Geometric and Potential Theoretic Results on {Lie} Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "412--437", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-019-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The main new results in this paper are contained in the geometric Theorems 1 and 2 of Section 0.1 below and they are related to previous results of M. Gromov and of myself (\cf\ \cite{1}, \cite{2}). These results are used to prove some general potential theoretic estimates on Lie groups (\cf\ Section 0.3) that are related to my previous work in the area (\cf\ \cite{3}, \cite{4}) and to some deep recent work of G. Alexopoulos (\cf\ \cite{5}, \cite{21}).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wallach:2000:SAT, author = "N. R. Wallach and J. Willenbring", title = "On Some $q$-Analogs of a Theorem of {Kostant--Rallis}", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "438--448", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-020-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In the first part of this paper generalizations of Hesselink's $q$-analog of Kostant's multiplicity formula for the action of a semisimple Lie group on the polynomials on its Lie algebra are given in the context of the Kostant-Rallis theorem. They correspond to the cases of real semisimple Lie groups with one conjugacy class of Cartan subgroup. In the second part of the paper a $q$-analog of the Kostant-Rallis theorem is given for the real group $\SL(4, \mathbb{R})$ (that is $\SO(4)$ acting on symmetric $4 \times 4$ matrices). This example plays two roles. First it contrasts with the examples of the first part. Second it has implications to the study of entanglement of mixed 2 qubit states in quantum computation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Adler:2000:IRA, author = "Jeffrey D. Adler and Alan Roche", title = "An Intertwining Result for $p$-adic Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "449--467", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-021-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a reductive $p$-adic group $G$, we compute the supports of the Hecke algebras for the $K$-types for $G$ lying in a certain frequently-occurring class. When $G$ is classical, we compute the intertwining between any two such $K$-types.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Edmunds:2000:TWE, author = "D. E. Edmunds and V. Kokilashvili and A. Meskhi", title = "Two-Weight Estimates for Singular Integrals Defined on Spaces of Homogeneous Type", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "468--502", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-022-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Two-weight inequalities of strong and weak type are obtained in the context of spaces of homogeneous type. Various applications are given, in particular to Cauchy singular integrals on regular curves.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gannon:2000:LMI, author = "Terry Gannon", title = "The Level 2 and 3 Modular Invariants for the Orthogonal Algebras", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "503--538", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-023-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The `1-loop partition function' of a rational conformal field theory is a sesquilinear combination of characters, invariant under a natural action of $\SL_2(\bbZ)$, and obeying an integrality condition. Classifying these is a clearly defined mathematical problem, and at least for the affine Kac--Moody algebras tends to have interesting solutions. This paper finds for each affine algebra $B_r^{(1)}$ and $D_r^{(1)}$ all of these at level $k\le 3$. Previously, only those at level 1 were classified. An extraordinary number of exceptionals appear at level 2---the $B_r^{(1)}$, $D_r^{(1)}$ level 2 classification is easily the most anomalous one known and this uniqueness is the primary motivation for this paper. The only level 3 exceptionals occur for $B_2^{(1)} \cong C_2^{(1)}$ and $D_7^{(1)}$. The $B_ {2,3}$ and $D_ {7,3}$ exceptionals are cousins of the ${\cal E}_6$-exceptional and $\E_8$-exceptional, respectively, in the A-D-E classification for $A_1^{(1)}$, while the level 2 exceptionals are related to the lattice invariants of affine $u(1)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jantzen:2000:SIR, author = "Chris Jantzen", title = "On Square-Integrable Representations of Classical $p$-adic Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "539--581", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-025-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we use Jacquet module methods to study the problem of classifying discrete series for the classical $p$-adic groups $\Sp(2n,F)$ and $\SO(2n+1,F)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jeffrey:2000:SGM, author = "Lisa C. Jeffrey and Jonathan Weitsman", title = "Symplectic Geometry of the Moduli Space of Flat Connections on a {Riemann} Surface: Inductive Decompositions and Vanishing Theorems", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "582--612", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-026-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper treats the moduli space ${\cal M}_ {g,1}(\Lambda)$ of representations of the fundamental group of a Riemann surface of genus $g$ with one boundary component which send the loop around the boundary to an element conjugate to $\exp \Lambda$, where $\Lambda$ is in the fundamental alcove of a Lie algebra. We construct natural line bundles over ${\cal M}_ {g,1} (\Lambda)$ and exhibit natural homology cycles representing the Poincar{\'e} dual of the first Chern class. We use these cycles to prove differential equations satisfied by the symplectic volumes of these spaces. Finally we give a bound on the degree of a nonvanishing element of a particular subring of the cohomology of the moduli space of stable bundles of coprime rank $k$ and degree $d$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ou:2000:SS, author = "Zhiming M. Ou and Kenneth S. Williams", title = "Small Solutions of $\phi_1 x_1^2 + \cdots + \phi_n x_n^2 = 0$", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "613--632", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-027-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\phi_1, \dots, \phi_n$ $(n\geq 2)$ be nonzero integers such that the equation \sum_{i=1}^n \phi_i x_i^2 = 0 is solvable in integers $x_1, \dots,x_n$ not all zero. It is shown that there exists a solution satisfying 0 < \sum_{i=1}^n |\phi_i| x_i^2 \leq 2 |\phi_1 \cdots \phi_n|, and that the constant 2 is best possible.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Walters:2000:CCF, author = "Samuel G. Walters", title = "{Chern} Characters of {Fourier} Modules", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "633--694", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-028-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $A_\theta$ denote the rotation algebra---the universal $C^\ast$-algebra generated by unitaries $U,V$ satisfying $VU=e^{2\pi i\theta}UV$, where $\theta$ is a fixed real number. Let $\sigma$ denote the Fourier automorphism of $A_\theta$ defined by $U\mapsto V$, $V\mapsto U^{-1}$, and let $B_\theta = A_\theta \rtimes_\sigma \mathbb{Z}/4\mathbb{Z}$ denote the associated $C^\ast$-crossed product. It is shown that there is a canonical inclusion $\mathbb{Z}^9 \hookrightarrow K_0(B_\theta)$ for each $\theta$ given by nine canonical modules. The unbounded trace functionals of $B_\theta$ (yielding the Chern characters here) are calculated to obtain the cyclic cohomology group of order zero $\HC^0(B_\theta)$ when $\theta$ is irrational. The Chern characters of the nine modules---and more importantly, the Fourier module---are computed and shown to involve techniques from the theory of Jacobi's theta functions. Also derived are explicit equations connecting unbounded traces across strong Morita equivalence, which turn out to be non-commutative extensions of certain theta function equations. These results provide the basis for showing that for a dense $G_\delta$ set of values of $\theta$ one has $K_0(B_\theta)\cong\mathbb{Z}^9$ and is generated by the nine classes constructed here.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Carey:2000:CNA, author = "A. Carey and M. Farber and V. Mathai", title = "Correspondences, {von Neumann} Algebras and Holomorphic {$L^2$} Torsion", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "695--736", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-030-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic $L^2$ torsion, which lies in the determinant line of the twisted $L^2$ Dolbeault cohomology and represents a volume element there. Here we utilise the theory of determinant lines of Hilbertian modules over finite von Neumann algebras as developed in \cite{CFM}. This specialises to the Ray--Singer-Quillen holomorphic torsion in the finite dimensional case. We compute a metric variation formula for the holomorphic $L^2$ torsion, which shows that it is {\em not\/} in general independent of the choice of Hermitian metrics on the complex manifold and on the holomorphic Hilbertian bundle, which are needed to define it. We therefore initiate the theory of correspondences of determinant lines, that enables us to define a relative holomorphic $L^2$ torsion for a pair of flat Hilbertian bundles, which we prove is independent of the choice of Hermitian metrics on the complex manifold and on the flat Hilbertian bundles.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gan:2000:ATM, author = "Wee Teck Gan", title = "An Automorphic Theta Module for Quaternionic Exceptional Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "737--756", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-031-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We construct an automorphic realization of the global minimal representation of quaternionic exceptional groups, using the theory of Eisenstein series, and use this for the study of theta correspondences.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hanani:2000:PNP, author = "Abdellah Hanani", title = "Le probl{\`e}me de {Neumann} pour certaines {\'e}quations du type de {Monge--Amp{\`e}re} sur une vari{\'e}t{\'e} riemannienne. ({French}) [{The} {Neumann} problem for certain {Monge--Amp{\`e}re}-type equations of {Riemannian} type]", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "757--788", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-032-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $(M_n,g)$ be a strictly convex riemannian manifold with $C^{\infty}$ boundary. We prove the existence\break of classical solution for the nonlinear elliptic partial differential equation of Monge-Amp{\`e}re:\break $\det (-u\delta^i_j + \nabla^i_ju) = F(x, \nabla u;u)$ in $M$ with a Neumann condition on the boundary of the form $\frac{\partial u}{\partial \nu} = \varphi (x,u)$, where $F \in C^{\infty} (TM \times \bbR)$ is an everywhere strictly positive function satisfying some assumptions, $\nu$ stands for the unit normal vector field and $\varphi \in C^{\infty} (\partial M \times \bbR)$ is a non-decreasing function in $u$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Kaminska:2000:DPP, author = "Anna Kami{\'n}ska and Mieczyslaw Mastylo", title = "The {Dunford--Pettis} Property for Symmetric Spaces", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "789--803", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-033-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A complete description of symmetric spaces on a separable measure space with the Dunford-Pettis property is given. It is shown that $\ell^1$, $c_0$ and $\ell^{\infty}$ are the only symmetric sequence spaces with the Dunford-Pettis property, and that in the class of symmetric spaces on $(0, \alpha)$, $0 < \alpha \leq \infty$, the only spaces with the Dunford-Pettis property are $L^1$, $L^{\infty}$, $L^1 \cap L^{\infty}$, $L^1 + L^{\infty}$, $(L^{\infty})^\circ$ and $(L^1 + L^{\infty})^\circ$, where $X^\circ$ denotes the norm closure of $L^1 \cap L^{\infty}$ in $X$. It is also proved that all Banach dual spaces of $L^1 \cap L^{\infty}$ and $L^1 + L^{\infty}$ have the Dunford-Pettis property. New examples of Banach spaces showing that the Dunford-Pettis property is not a three-space property are also presented. As applications we obtain that the spaces $(L^1 + L^{\infty})^\circ$ and $(L^{\infty})^\circ$ have a unique symmetric structure, and we get a characterization of the Dunford-Pettis property of some K{\"o}the-Bochner spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kottwitz:2000:DIT, author = "Robert E. Kottwitz and Jonathan D. Rogawski", title = "The Distributions in the Invariant Trace Formula Are Supported on Characters", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "804--814", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-034-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "J. Arthur put the trace formula in invariant form for all connected reductive groups and certain disconnected ones. However his work was written so as to apply to the general disconnected case, modulo two missing ingredients. This paper supplies one of those missing ingredients, namely an argument in Galois cohomology of a kind first used by D. Kazhdan in the connected case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lubinsky:2000:MMM, author = "D. S. Lubinsky", title = "On the Maximum and Minimum Modulus of Rational Functions", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "815--832", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-035-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We show that if $m$, $n\geq 0$, $\lambda > 1$, and $R$ is a rational function with numerator, denominator of degree $\leq m$, $n$, respectively, then there exists a set $\mathcal{S}\subset [0,1] $ of linear measure $\geq \frac{1}{4}\exp (-\frac{13}{\log \lambda})$ such that for $r\in \mathcal{S}$, \[ \max_{|z| =r}| R(z)| / \min_{|z| =r} | R(z) |\leq \lambda ^{m+n}. \] Here, one may not replace $\frac{1}{4}\exp ( -\frac{13}{\log \lambda})$ by $\exp (-\frac{2-\varepsilon}{\log \lambda})$, for any $\varepsilon > 0$. As our motivating application, we prove a convergence result for diagonal Pad{\'e} approximants for functions meromorphic in the unit ball.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Minac:2000:GUQ, author = "J{\'a}n Min{\'a}c and Tara L. Smith", title = "{$W$}-Groups under Quadratic Extensions of Fields", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "833--848", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-036-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "To each field $F$ of characteristic not $2$, one can associate a certain Galois group $\G_F$, the so-called W-group of $F$, which carries essentially the same information as the Witt ring $W(F)$ of $F$. In this paper we investigate the connection between $\wg$ and $\G_{F(\sqrt{a})}$, where $F(\sqrt{a})$ is a proper quadratic extension of $F$. We obtain a precise description in the case when $F$ is a pythagorean formally real field and $a = -1$, and show that the W-group of a proper field extension $K/F$ is a subgroup of the W-group of $F$ if and only if $F$ is a formally real pythagorean field and $K = F(\sqrt{-1})$. This theorem can be viewed as an analogue of the classical Artin--Schreier's theorem describing fields fixed by finite subgroups of absolute Galois groups. We also obtain precise results in the case when $a$ is a double-rigid element in $F$. Some of these results carry over to the general setting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sukochev:2000:OEF, author = "F. A. Sukochev", title = "Operator Estimates for {Fredholm} Modules", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "849--896", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-037-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study estimates of the type \Vert \phi(D) - \phi(D_0) \Vert_{\emt} \leq C \cdot \Vert D - D_0 \Vert^{\alpha}, \quad \alpha = \frac12, 1 where $\phi(t) = t(1 + t^2)^{-1/2}$, $D_0 = D_0^*$ is an unbounded linear operator affiliated with a semifinite von Neumann algebra $\calM$, $D - D_0$ is a bounded self-adjoint linear operator from $\calM$ and $(1 + D_0^2)^{-1/2} \in \emt$, where $\emt$ is a symmetric operator space associated with $\calM$. In particular, we prove that $\phi(D) - \phi(D_0)$ belongs to the non-commutative $L_p$-space for some $p \in (1, \infty)$, provided $(1 + D_0^2)^{-1/2}$ belongs to the non-commutative weak $L_r$-space for some $r \in [1,p)$. In the case $\calM = \calB (\calH)$ and $1 \leq p \leq 2$, we show that this result continues to hold under the weaker assumption $(1 + D_0^2)^{-1/2} \in \calC_p$. This may be regarded as an odd counterpart of A. Connes' result for the case of even Fredholm modules.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Christiansen:2000:HOS, author = "T. J. Christiansen and M. S. Joshi", title = "Higher Order Scattering on Asymptotically {Euclidean} Manifolds", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "897--919", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-038-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time $\pi$ on the boundary. Furthermore, it is shown that on $\Real^n$ the asymptotics of certain short-range perturbations of $\Delta^k$ can be recovered from the scattering matrix at a finite number of energies.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Evans:2000:RIL, author = "W. D. Evans and B. Opic", title = "Real {Interpolation} with Logarithmic Functors and Reiteration", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "920--960", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-039-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We present {``reiteration theorems''} with limiting values $\theta=0$ and $\theta = 1$ for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ismail:2000:AES, author = "Mourad E. H. Ismail and Jim Pitman", title = "Algebraic Evaluations of Some {Euler} Integrals, Duplication Formulae for {Appell}'s Hypergeometric Function {$F_1$}, and {Brownian} Variations", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "961--981", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-040-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Explicit evaluations of the symmetric Euler integral $\int_0^1 u^{\alpha} (1-u)^{\alpha} f(u) du$ are obtained for some particular functions $f$. These evaluations are related to duplication formulae for Appell's hypergeometric function $F_1$ which give reductions of $F_1 (\alpha, \beta, \beta, 2 \alpha, y, z)$ in terms of more elementary functions for arbitrary $\beta$ with $z = y/(y-1)$ and for $\beta = \alpha + \half$ with arbitrary $y$, $z$. These duplication formulae generalize the evaluations of some symmetric Euler integrals implied by the following result: if a standard Brownian bridge is sampled at time $0$, time $1$, and at $n$ independent random times with uniform distribution on $[0,1]$, then the broken line approximation to the bridge obtained from these $n+2$ values has a total variation whose mean square is $n(n+1)/(2n+1)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Larusson:2000:HFS, author = "Finnur L{\'a}russon", title = "Holomorphic Functions of Slow Growth on Nested Covering Spaces of Compact Manifolds", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "982--998", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-041-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $Y$ be an infinite covering space of a projective manifold $M$ in $\P^N$ of dimension $n\geq 2$. Let $C$ be the intersection with $M$ of at most $n-1$ generic hypersurfaces of degree $d$ in $\mathbb{P}^N$. The preimage $X$ of $C$ in $Y$ is a connected submanifold. Let $\phi$ be the smoothed distance from a fixed point in $Y$ in a metric pulled up from $M$. Let $\O_\phi(X)$ be the Hilbert space of holomorphic functions $f$ on $X$ such that $f^2 e^{-\phi}$ is integrable on $X$, and define $\O_\phi(Y)$ similarly. Our main result is that (under more general hypotheses than described here) the restriction $\O_\phi(Y) \to \O_\phi(X)$ is an isomorphism for $d$ large enough. This yields new examples of Riemann surfaces and domains of holomorphy in $\C^n$ with corona. We consider the important special case when $Y$ is the unit ball $\B$ in $\C^n$, and show that for $d$ large enough, every bounded holomorphic function on $X$ extends to a unique function in the intersection of all the nontrivial weighted Bergman spaces on $\B$. Finally, assuming that the covering group is arithmetic, we establish three dichotomies concerning the extension of bounded holomorphic and harmonic functions from $X$ to $\B$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mankiewicz:2000:CGO, author = "Piotr Mankiewicz", title = "Compact Groups of Operators on Subproportional Quotients of $l^m_1$", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "999--1017", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-042-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is proved that a {``typical''} $n$-dimensional quotient $X_n$ of $l^m_1$ with $n = m^{\sigma}$, $0 < \sigma < 1$, has the property \Average \int_G \|Tx\|_{X_n} \,dh_G(T) \geq \frac{c}{\sqrt{n\log^3 n}} \biggl( n - \int_G |\tr T| \,dh_G (T) \biggr), for every compact group $G$ of operators acting on $X_n$, where $d_G(T)$ stands for the normalized Haar measure on $G$ and the average is taken over all extreme points of the unit ball of $X_n$. Several consequences of this estimate are presented.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Reichstein:2000:EDA, author = "Zinovy Reichstein and Boris Youssin", title = "Essential Dimensions of Algebraic Groups and a Resolution Theorem for {$G$}-Varieties", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1018--1056", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-043-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be an algebraic group and let $X$ be a generically free $G$-variety. We show that $X$ can be transformed, by a sequence of blowups with smooth $G$-equivariant centers, into a $G$-variety $X'$ with the following property the stabilizer of every point of $X'$ is isomorphic to a semidirect product $U x A$ of a unipotent group $U$ and a diagonalizable group $A$. As an application of this result, we prove new lower bounds on essential dimensions of some algebraic groups. We also show that certain polynomials in one variable cannot be simplified by a Tschirnhaus transformation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Urakawa:2000:SIG, author = "Hajime Urakawa", title = "The Spectrum of an Infinite Graph", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1057--1084", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-044-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential) spectrum for several examples of infinite graphs.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Xing:2000:CMA, author = "Yang Xing", title = "Complex {Monge--Amp{\`e}re} Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1085--1100", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-045-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give a characterization of bounded plurisubharmonic functions by using their complex Monge--Amp{\`e}re measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge--Amp{\`e}re measure of some bounded plurisubharmonic function.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhang:2000:DSC, author = "Yuanli Zhang", title = "Discrete Series of Classical Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1101--1120", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-046-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G_n$ be the split classical groups $\Sp(2n)$, $\SO(2n+1)$ and $\SO(2n)$ defined over a $p$-adic field F or the quasi-split classical groups $U(n,n)$ and $U(n+1,n)$ with respect to a quadratic extension $E/F$. We prove the self-duality of unitary supercuspidal data of standard Levi subgroups of $G_n(F)$ which give discrete series representations of $G_n(F)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ballantine:2000:RTB, author = "Cristina M. Ballantine", title = "{Ramanujan} Type Buildings", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1121--1148", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-047-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We will construct a finite union of finite quotients of the affine building of the group $\GL_3$ over the field of $p$-adic numbers $\mathbb{Q}_p$. We will view this object as a hypergraph and estimate the spectrum of its underlying graph.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ban:2000:CRQ, author = "Chunsheng Ban and Lee J. McEwan", title = "Canonical Resolution of a Quasi-ordinary Surface Singularity", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1149--1163", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-048-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We describe the embedded resolution of an irreducible quasi-ordinary surface singularity $(V,p)$ which results from applying the canonical resolution of Bierstone-Milman to $(V,p)$. We show that this process depends solely on the characteristic pairs of $(V,p)$, as predicted by Lipman. We describe the process explicitly enough that a resolution graph for $f$ could in principle be obtained by computer using only the characteristic pairs.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Elliott:2000:POG, author = "George A. Elliott and Jesper Villadsen", title = "Perforated Ordered {$\K_0$}-Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1164--1191", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-049-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A simple $\C^*$-algebra is constructed for which the Murray-von Neumann equivalence classes of projections, with the usual addition---induced by addition of orthogonal projections---form the additive semi-group \{0,2,3, \dots\}. (This is a particularly simple instance of the phenomenon of perforation of the ordered $\K_0$-group, which has long been known in the commutative case---for instance, in the case of the four-sphere---and was recently observed by the second author in the case of a simple $\C^*$-algebra.)", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Herb:2000:OIA, author = "Rebecca A. Herb", title = "Orbital Integrals on $p$-Adic {Lie} Algebras", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1192--1220", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-050-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a connected reductive $p$-adic group and let $\frakg$ be its Lie algebra. Let $\calO$ be any $G$-orbit in $\frakg$. Then the orbital integral $\mu_{\calO}$ corresponding to $\calO$ is an invariant distribution on $\frakg $, and Harish-Chandra proved that its Fourier transform $\hat \mu_{\calO}$ is a locally constant function on the set $\frakg'$ of regular semisimple elements of $\frakg$. If $\frakh$ is a Cartan subalgebra of $\frakg$, and $\omega$ is a compact subset of $\frakh\cap\frakg'$, we give a formula for $\hat \mu_{\calO}(tH)$ for $H\in\omega$ and $t\in F^ \times $ sufficiently large. In the case that $\calO$ is a regular semisimple orbit, the formula is already known by work of Waldspurger. In the case that $\calO$ is a nilpotent orbit, the behavior of $\hat\mu_{\calO}$ at infinity is already known because of its homogeneity properties. The general case combines aspects of these two extreme cases. The formula for $\hat\mu _{\calO}$ at infinity can be used to formulate a ``theory of the constant term'' for the space of distributions spanned by the Fourier transforms of orbital integrals. It can also be used to show that the Fourier transforms of orbital integrals are ``linearly independent at infinity.''", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hopenwasser:2000:NRT, author = "Alan Hopenwasser and Justin R. Peters and Stephen C. Power", title = "Nest Representations of {TAF} Algebras", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1221--1234", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-051-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A nest representation of a strongly maximal TAF algebra $A$ with diagonal $D$ is a representation $\pi$ for which $\lat \pi(A)$ is totally ordered. We prove that $\ker \pi$ is a meet irreducible ideal if the spectrum of $A$ is totally ordered or if (after an appropriate similarity) the von Neumann algebra $\pi(D)''$ contains an atom.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hurtubise:2000:RWF, author = "J. C. Hurtubise and L. C. Jeffrey", title = "Representations with Weighted Frames and Framed Parabolic Bundles", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1235--1268", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-052-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "There is a well-known correspondence (due to Mehta and Seshadri in the unitary case, and extended by Bhosle and Ramanathan to other groups), between the symplectic variety $M_h$ of representations of the fundamental group of a punctured Riemann surface into a compact connected Lie group $G$, with fixed conjugacy classes $h$ at the punctures, and a complex variety ${\cal M}_h$ of holomorphic bundles on the unpunctured surface with a parabolic structure at the puncture points. For $G = \SU(2)$, we build a symplectic variety $P$ of pairs (representations of the fundamental group into $G$, ``weighted frame'' at the puncture points), and a corresponding complex variety ${\cal P}$ of moduli of ``framed parabolic bundles'', which encompass respectively all of the spaces $M_h$, ${\cal M}_h$, in the sense that one can obtain $M_h$ from $P$ by symplectic reduction, and ${\cal M}_h$ from ${\cal P}$ by a complex quotient. This allows us to explain certain features of the toric geometry of the $\SU(2)$ moduli spaces discussed by Jeffrey and Weitsman, by giving the actual toric variety associated with their integrable system.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Spriano:2000:WRE, author = "Luca Spriano", title = "Well Ramified Extensions of Complete Discrete Valuation Fields with Applications to the {Kato} Conductor", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1269--1309", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-053-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study extensions $L/K$ of complete discrete valuation fields $K$ with residue field $\oK$ of characteristic $p > 0$, which we do not assume to be perfect. Our work concerns ramification theory for such extensions, in particular we show that all classical properties which are true under the hypothesis {\em ``the residue field extension $\oL/\oK$ is separable''} are still valid under the more general hypothesis that the valuation ring extension is monogenic. We also show that conversely, if classical ramification properties hold true for an extension $L/K$, then the extension of valuation rings is monogenic. These are the ``{\em well ramified}'' extensions. We show that there are only three possible types of well ramified extensions and we give examples. In the last part of the paper we consider, for the three types, Kato's generalization of the conductor, which we show how to bound in certain cases.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yagunov:2000:HHP, author = "Serge Yagunov", title = "On the Homology of {$\GL_n$} and Higher Pre-{Bloch} Groups", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1310--1338", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-054-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For every integer $n > 1$ and infinite field $F$ we construct a spectral sequence converging to the homology of $\GL_n(F)$ relative to the group of monomial matrices $\GM_n(F)$. Some entries in $E^2$-terms of these spectral sequences may be interpreted as a natural generalization of the Bloch group to higher dimensions. These groups may be characterized as homology of $\GL_n$ relatively to $\GL_{n-1}$ and $\GM_n$. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2000:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2000 --- pour 2000", journal = j-CAN-J-MATH, volume = "52", number = "??", pages = "1339--1343", month = "????", year = "2000", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2000-055-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:09 MDT 2011", bibsource = "http://cms.math.ca/cjm/v52/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bell:2001:EGG, author = "J. P. Bell", title = "The Equivariant {Grothendieck} Groups of the {Russell--Koras} Threefolds", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "3--32", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-001-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic $\mathbb{C}^*$-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Borwein:2001:MFP, author = "Peter Borwein and Kwok-Kwong Stephen Choi", title = "Merit Factors of Polynomials Formed by {Jacobi} Symbols", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "33--50", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-002-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give explicit formulas for the $L_4$ norm (or equivalently for the merit factors) of various sequences of polynomials related to the polynomials f(z) := \sum_{n=0}^{N-1} \leq n {N} z^n. and f_t(z) = \sum_{n=0}^{N-1} \leq {n+t}{N} z^n. where $(\frac{\cdot}{N})$ is the Jacobi symbol. Two cases of particular interest are when $N = pq$ is a product of two primes and $p = q+2$ or $p = q+4$. This extends work of H{\o}holdt, Jensen and Jensen and of the authors. This study arises from a number of conjectures of Erd\H{o}s, Littlewood and others that concern the norms of polynomials with $-1,1$ coefficients on the disc. The current best examples are of the above form when $N$ is prime and it is natural to see what happens for composite $N$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dean:2001:CFP, author = "Andrew Dean", title = "A Continuous Field of Projectionless {$C^*$}-Algebras", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "51--72", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-003-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We use some results about stable relations to show that some of the simple, stable, projectionless crossed products of $O_2$ by $\bR$ considered by Kishimoto and Kumjian are inductive limits of type I $C^*$-algebras. The type I $C^*$-algebras that arise are pullbacks of finite direct sums of matrix algebras over the continuous functions on the unit interval by finite dimensional $C^*$-algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fukui:2001:STW, author = "Toshizumi Fukui and Laurentiu Paunescu", title = "Stratification Theory from the Weighted Point of View", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "73--97", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-004-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we investigate stratification theory in terms of the defining equations of strata and maps (without tube systems), offering a concrete approach to show that some given family is topologically trivial. In this approach, we consider a weighted version of $(w)$-regularity condition and Kuo's ratio test condition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Khuri-Makdisi:2001:CAC, author = "Kamal Khuri-Makdisi", title = "On the Curves Associated to Certain Rings of Automorphic Forms", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "98--121", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-005-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In a 1987 paper, Gross introduced certain curves associated to a definite quaternion algebra $B$ over $\Q$; he then proved an analog of his result with Zagier for these curves. In Gross' paper, the curves were defined in a somewhat {\em ad hoc\/} manner. In this article, we present an interpretation of these curves as projective varieties arising from graded rings of automorphic forms on $B^\times$, analogously to the construction in the Satake compactification. To define such graded rings, one needs to introduce a ``multiplication'' of automorphic forms that arises from the representation ring of $B^\times$. The resulting curves are unions of projective lines equipped with a collection of Hecke correspondences. They parametrize two-dimensional complex tori with quaternionic multiplication. In general, these complex tori are not abelian varieties; they are algebraic precisely when they correspond to $\CM$ points on these curves, and are thus isogenous to a product $E \times E$, where $E$ is an elliptic curve with complex multiplication. For these $\CM$ points one can make a relation between the action of the $p$-th Hecke operator and Frobenius at $p$, similar to the well-known congruence relation of Eichler and Shimura.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Levy:2001:TIP, author = "Jason Levy", title = "A Truncated Integral of the {Poisson} Summation Formula", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "122--160", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-006-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a reductive algebraic group defined over $\bQ$, with anisotropic centre. Given a rational action of $G$ on a finite-dimensional vector space $V$, we analyze the truncated integral of the theta series corresponding to a Schwartz-Bruhat function on $V(\bA)$. The Poisson summation formula then yields an identity of distributions on $V(\bA)$. The truncation used is due to Arthur.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lin:2001:CST, author = "Huaxin Lin", title = "Classification of Simple Tracially {AF} {$C^*$}-Algebras", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "161--194", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-007-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that pre-classifiable (see 3.1) simple nuclear tracially AF \CA s (TAF) are classified by their $K$-theory. As a consequence all simple, locally AH and TAF \CA s are in fact AH algebras (it is known that there are locally AH algebras that are not AH). We also prove the following Rationalization Theorem. Let $A$ and $B$ be two unital separable nuclear simple TAF \CA s with unique normalized traces satisfying the Universal Coefficient Theorem. If $A$ and $B$ have the same (ordered and scaled) $K$-theory and $K_0 (A)_+$ is locally finitely generated, then $A \otimes Q \cong B \otimes Q$, where $Q$ is the UHF-algebra with the rational $K_0$. Classification results (with restriction on $K_0$-theory) for the above \CA s are also obtained. For example, we show that, if $A$ and $B$ are unital nuclear separable simple TAF \CA s with the unique normalized trace satisfying the UCT and with $K_1(A) = K_1(B)$, and $A$ and $B$ have the same rational (scaled ordered) $K_0$, then $A \cong B$. Similar results are also obtained for some cases in which $K_0$ is non-divisible such as $K_0(A) = \mathbf{Z} [1/2]$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mokler:2001:SMS, author = "Claus Mokler", title = "On the {Steinberg} Map and {Steinberg} Cross-Section for a Symmetrizable Indefinite {Kac--Moody} Group", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "195--211", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-008-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a symmetrizable indefinite Kac--Moody group over $\C$. Let $\Tr_{\La_1}, \dots, \Tr_{\La_{2n-l}}$ be the characters of the fundamental irreducible representations of $G$, defined as convergent series on a certain part $G^{\tralg} \subseteq G$. Following Steinberg in the classical case and Br{\"u}chert in the affine case, we define the Steinberg map $\chi := (\Tr_{\La_1}, \dots, \Tr_{\La_{2n-l}})$ as well as the Steinberg cross section $C$, together with a natural parametrisation $\omega \colon \C^n \times (\C^\times)^{\,n-l} \to C$. We investigate the local behaviour of $\chi$ on $C$ near $\omega \bigl( (0, \dots,0) \times (1, \dots,1) \bigr)$, and we show that there exists a neighborhood of $(0, \dots,0) \times (1, \dots,1)$, on which $\chi \circ \omega$ is a regular analytical map, satisfying a certain functional identity. This identity has its origin in an action of the center of $G$ on $C$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Puppe:2001:GAC, author = "V. Puppe", title = "Group Actions and Codes", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "212--224", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-009-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A $\mathbb{Z}_2$-action with ``maximal number of isolated fixed points'' ({\em i.e.}, with only isolated fixed points such that $\dim_k (\oplus_i H^i(M;k)) =|M^{\mathbb{Z}_2}|, k = \mathbb{F}_2)$ on a $3$-dimensional, closed manifold determines a binary self-dual code of length $=|M^{\mathbb{Z}_2}|$. In turn this code determines the cohomology algebra $H^*(M;k)$ and the equivariant cohomology $H^*_ {\mathbb{Z}_2}(M;k)$. Hence, from results on binary self-dual codes one gets information about the cohomology type of $3$-manifolds which admit involutions with maximal number of isolated fixed points. In particular, ``most'' cohomology types of closed $3$-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, {\em e.g.}, one gets that ``most'' cohomology types (over $\mathbb{F}_2)$ of closed $3$-manifolds do not admit a non-trivial involution.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Britten:2001:TPR, author = "D. J. Britten and F. W. Lemire", title = "Tensor Product Realizations of Simple Torsion Free Modules", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "225--243", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-010-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\calG$ be a finite dimensional simple Lie algebra over the complex numbers $C$. Fernando reduced the classification of infinite dimensional simple $\calG$-modules with a finite dimensional weight space to determining the simple torsion free $\calG$-modules for $\calG$ of type $A$ or $C$. These modules were determined by Mathieu and using his work we provide a more elementary construction realizing each one as a submodule of an easily constructed tensor product module.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Goldberg:2001:TSQ, author = "David Goldberg and Freydoon Shahidi", title = "On the Tempered Spectrum of Quasi-Split Classical Groups {II}", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "244--277", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-011-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We determine the poles of the standard intertwining operators for a maximal parabolic subgroup of the quasi-split unitary group defined by a quadratic extension $E/F$ of $p$-adic fields of characteristic zero. We study the case where the Levi component $M \simeq \GL_n (E) \times U_m (F)$, with $n \equiv m$ $(\mod 2)$. This, along with earlier work, determines the poles of the local Rankin-Selberg product $L$-function $L(s, \tau' \times \tau)$, with $\tau'$ an irreducible unitary supercuspidal representation of $\GL_n (E)$ and $\tau$ a generic irreducible unitary supercuspidal representation of $U_m (F)$. The results are interpreted using the theory of twisted endoscopy.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Helminck:2001:DTK, author = "G. F. Helminck and J. W. van de Leur", title = "{Darboux} Transformations for the {KP} Hierarchy in the {Segal--Wilson} Setting", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "278--309", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-012-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper it is shown that inclusions inside the Segal-Wilson Grassmannian give rise to Darboux transformations between the solutions of the $\KP$ hierarchy corresponding to these planes. We present a closed form of the operators that procure the transformation and express them in the related geometric data. Further the associated transformation on the level of $\tau$-functions is given.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ito:2001:PRC, author = "Hiroshi Ito", title = "On a Product Related to the Cubic {Gauss} Sum, {III}", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "310--324", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-013-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We have seen, in the previous works [5], [6], that the argument of a certain product is closely connected to that of the cubic Gauss sum. Here the absolute value of the product will be investigated.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Matui:2001:EOC, author = "Hiroki Matui", title = "Ext and OrderExt Classes of Certain Automorphisms of {$C^*$}-Algebras Arising from {Cantor} Minimal Systems", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "325--354", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-014-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Giordano, Putnam and Skau showed that the transformation group $C^*$-algebra arising from a Cantor minimal system is an $AT$-algebra, and classified it by its $K$-theory. For approximately inner automorphisms that preserve $C(X)$, we will determine their classes in the Ext and OrderExt groups, and introduce a new invariant for the closure of the topological full group. We will also prove that every automorphism in the kernel of the homomorphism into the Ext group is homotopic to an inner automorphism, which extends Kishimoto's result.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nica:2001:DEF, author = "Alexandru Nica and Dimitri Shlyakhtenko and Roland Speicher", title = "{$R$}-Diagonal Elements and Freeness With Amalgamation", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "355--381", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-015-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The concept of $R$-diagonal element was introduced in \cite{NS2}, and was subsequently found to have applications to several problems in free probability. In this paper we describe a new approach to $R$-diagonality, which relies on freeness with amalgamation. The class of $R$-diagonal elements is enlarged to contain examples living in non-tracial $*$-probability spaces, such as the generalized circular elements of \cite{Sh1}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pivato:2001:BSS, author = "Marcus Pivato", title = "Building a Stationary Stochastic Process From a Finite-Dimensional Marginal", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "382--413", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-016-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "If $\mathfrak{A}$ is a finite alphabet, $\sU \subset\mathbb{Z}^D$, and $\mu_\sU$ is a probability measure on $\mathfrak{A}^\sU$ that ``looks like'' the marginal projection of a stationary stochastic process on $\mathfrak{A}^{\mathbb{Z}^D}$, then can we ``extend'' $\mu_\sU$ to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when $D=1$, we provide some sufficient conditions and some necessary conditions for $\mu_\sU$ to be extendible for $D > 1$, and show that, in general, the problem is not formally decidable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rivat:2001:NPF, author = "Jo{\"e}l Rivat and Patrick Sargos", title = "Nombres premiers de la forme $\floor{n^c}$. ({French}) [{Prime} numbers of the form $\floor{n^c}$]", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "414--433", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-017-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For $c > 1$ we denote by $\pi_c(x)$ the number of integers $n \leq x$ such that $\floor{n^c}$ is prime. In 1953, Piatetski-Shapiro has proved that $\pi_c(x) \sim \frac{x}{c\log x}$, $x \rightarrow +\infty$ holds for $c < 12/11$. Many authors have extended this range, which measures our progress in exponential sums techniques. In this article we obtain $c < 1.16117\dots\;$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{vanderPoorten:2001:VDE, author = "Alfred J. van der Poorten and Kenneth S. Williams", title = "Values of the {Dedekind} Eta Function at Quadratic Irrationalities: Corrigendum", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "434--448", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-018-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{vanderPoorten:1999:VDE}.", abstract = "Habib Muzaffar of Carleton University has pointed out to the authors that in their paper [A] only the result \[ \pi_{K,d}(x)+\pi_{K^{-1},d}(x)=\frac{1}{h(d)}\frac{x}{\log x}+O_{K,d}\Bigl(\frac {x}{\log^2x}\Bigr) \] follows from the prime ideal theorem with remainder for ideal classes, and not the stronger result \[ \pi_{K,d}(x)=\frac{1}{2h(d)}\frac{x}{\log x}+O_{K,d}\Bigl(\frac {x}{\log^2x}\Bigr) \] stated in Lemma 5.2. This necessitates changes in Sections 5 and 6 of [A]. The main results of the paper are not affected by these changes. It should also be noted that, starting on page 177 of [A], each and every occurrence of $o(s-1)$ should be replaced by $o(1)$. Sections 5 and 6 of [A] have been rewritten to incorporate the above mentioned correction and are given below. They should replace the original Sections 5 and 6 of [A].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Akbary:2001:DRP, author = "Amir Akbary and V. Kumar Murty", title = "Descending Rational Points on Elliptic Curves to Smaller Fields", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "449--469", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-019-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we study the Mordell-Weil group of an elliptic curve as a Galois module. We consider an elliptic curve $E$ defined over a number field $K$ whose Mordell-Weil rank over a Galois extension $F$ is $1$, $2$ or $3$. We show that $E$ acquires a point (points) of infinite order over a field whose Galois group is one of $C_n \times C_m$ ($n= 1, 2, 3, 4, 6, m= 1, 2$), $D_n \times C_m$ ($n= 2, 3, 4, 6, m= 1, 2$), $A_4 \times C_m$ ($m=1,2$), $S_4 \times C_m$ ($m=1,2$). Next, we consider the case where $E$ has complex multiplication by the ring of integers $\o$ of an imaginary quadratic field $\k$ contained in $K$. Suppose that the $\o$-rank over a Galois extension $F$ is $1$ or $2$. If $\k\neq\Q(\sqrt{-1})$ and $\Q(\sqrt{-3})$ and $h_{\k}$ (class number of $\k$) is odd, we show that $E$ acquires positive $\o$-rank over a cyclic extension of $K$ or over a field whose Galois group is one of $\SL_2(\Z/3\Z)$, an extension of $\SL_2(\Z/3\Z)$ by $\Z/2\Z$, or a central extension by the dihedral group. Finally, we discuss the relation of the above results to the vanishing of $L$-functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bauschke:2001:HPC, author = "Heinz H. Bauschke and Osman G{\"u}ler and Adrian S. Lewis and Hristo S. Sendov", title = "Hyperbolic Polynomials and Convex Analysis", journal = j-CAN-J-MATH, volume = "53", number = "3", pages = "470--488", month = jun, year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-020-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "90C46 (15A45 52A41)", MRnumber = "MR1827817 (2002c:90099)", MRreviewer = "Vaithilingam Jeyakumar", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib; Karlsruhe bibliography archive", abstract = "A homogeneous real polynomial $p$ is {\em hyperbolic} with respect to a given vector $d$ if the univariate polynomial $t \mapsto p(x-td)$ has all real roots for all vectors $x$. Motivated by partial differential equations, G{\aa}rding proved in 1951 that the largest such root is a convex function of $x$, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, and use it to generalize G{\aa}rding's result to arbitrary symmetric functions of the roots. Many classical and recent inequalities follow easily. We develop various convex-analytic tools for such symmetric functions, of interest in interior-point methods for optimization problems over related cones.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bojanov:2001:BPL, author = "Borislav D. Bojanov and Werner Hau{\ss}mann and Geno P. Nikolov", title = "Bivariate Polynomials of Least Deviation from Zero", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "489--505", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-021-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Bivariate polynomials with a fixed leading term $x^m y^n$, which deviate least from zero in the uniform or $L^2$-norm on the unit disk $D$ (resp. a triangle) are given explicitly. A similar problem in $L^p$, $1 \le p \le \infty$, is studied on $D$ in the set of products of linear polynomials.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Davidson:2001:IDN, author = "Kenneth R. Davidson and David W. Kribs and Miron E. Shpigel", title = "Isometric Dilations of Non-Commuting Finite Rank $n$-Tuples", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "506--545", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-022-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A contractive $n$-tuple $A=(A_1, \dots,A_n)$ has a minimal joint isometric dilation $S=\break (S_1, \dots,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When $A$ acts on a finite dimensional space, the $\wot$-closed nonself-adjoint algebra $\fS$ generated by $S$ is completely described in terms of the properties of $A$. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra $\fS$ is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an $n$-tuple $B$ of $d\times d$ matrices is similar to an irreducible $n$-tuple $A$ if and only if a certain finite set of polynomials vanish on $B$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Erlijman:2001:MSB, author = "Juliana Erlijman", title = "Multi-Sided Braid Type Subfactors", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "546--591", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-023-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We generalise the two-sided construction of examples of pairs of subfactors of the hyperfinite II$_1$ factor $R$ in [E1]---which arise by considering unitary braid representations with certain properties---to multi-sided pairs. We show that the index for the multi-sided pair can be expressed as a power of that for the two-sided pair. This construction can be applied to the natural examples---where the braid representations are obtained in connection with the representation theory of Lie algebras of types $A$, $B$, $C$, $D$. We also compute the (first) relative commutants.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Perera:2001:ISM, author = "Francesc Perera", title = "Ideal Structure of Multiplier Algebras of Simple {$C^*$}-algebras With Real Rank Zero", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "592--630", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-025-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give a description of the monoid of Murray--von Neumann equivalence classes of projections for multiplier algebras of a wide class of $\sigma$-unital simple $C^\ast$-algebras $A$ with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of the multiplier algebra $\mul$, is therefore analyzed. In important cases it is shown that, if $A$ has finite scale then the quotient of $\mul$ modulo any closed ideal $I$ that properly contains $A$ has stable rank one. The intricacy of the ideal structure of $\mul$ is reflected in the fact that $\mul$ can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Walters:2001:TNC, author = "Samuel G. Walters", title = "{$K$}-Theory of Non-Commutative Spheres Arising from the {Fourier} Automorphism", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "631--674", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-026-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a dense $G_\delta$ set of real parameters $\theta$ in $[0,1]$ (containing the rationals) it is shown that the group $K_0 (A_\theta \rtimes_\sigma \mathbb{Z}_4)$ is isomorphic to $\mathbb{Z}^9$, where $A_\theta$ is the rotation C*-algebra generated by unitaries $U$, $V$ satisfying $VU = e^{2\pi i\theta} UV$ and $\sigma$ is the Fourier automorphism of $A_\theta$ defined by $\sigma(U) = V$, $\sigma(V) = U^{-1}$. More precisely, an explicit basis for $K_0$ consisting of nine canonical modules is given. (A slight generalization of this result is also obtained for certain separable continuous fields of unital C*-algebras over $[0,1]$.) The Connes Chern character $\ch \colon K_0 (A_\theta \rtimes_\sigma \mathbb{Z}_4) \to H^{\ev} (A_\theta \rtimes_\sigma \mathbb{Z}_4)^*$ is shown to be injective for a dense $G_\delta$ set of parameters $\theta$. The main computational tool in this paper is a group homomorphism $\vtr \colon K_0 (A_\theta \rtimes_\sigma \mathbb{Z}_4) \to \mathbb{R}^8 \times \mathbb{Z}$ obtained from the Connes Chern character by restricting the functionals in its codomain to a certain nine-dimensional subspace of $H^{\ev} (A_\theta \rtimes_\sigma \mathbb{Z}_4)$. The range of $\vtr$ is fully determined for each $\theta$. (We conjecture that this subspace is all of $H^{\ev}$.)", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ban:2001:JMP, author = "Dubravka Ban", title = "{Jacquet} Modules of Parabolically Induced Representations and {Weyl} Groups", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "675--695", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-027-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The representation parabolically induced from an irreducible supercuspidal representation is considered. Irreducible components of Jacquet modules with respect to induction in stages are given. The results are used for consideration of generalized Steinberg representations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Currie:2001:APA, author = "J. Currie and V. Linek", title = "Avoiding Patterns in the {Abelian} Sense", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "696--714", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-028-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some properties of $\o$-words avoiding these patterns.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cushman:2001:DSO, author = "Richard Cushman and J{\k{e}}drzej {\'S}niatycki", title = "Differential Structure of Orbit Spaces", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "715--755", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-029-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See erratum \cite{Cushman:2003:DSO}.", abstract = "We present a new approach to singular reduction of Hamiltonian systems with symmetries. The tools we use are the category of differential spaces of Sikorski and the Stefan-Sussmann theorem. The former is applied to analyze the differential structure of the spaces involved and the latter is used to prove that some of these spaces are smooth manifolds. Our main result is the identification of accessible sets of the generalized distribution spanned by the Hamiltonian vector fields of invariant functions with singular reduced spaces. We are also able to describe the differential structure of a singular reduced space corresponding to a coadjoint orbit which need not be locally closed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Froese:2001:CUB, author = "Richard Froese", title = "Correction to: {``Upper Bounds for the Resonance Counting Function of Schr{\"o}dinger Operators in Odd Dimensions''}", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "756--757", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-030-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{Froese:1998:UBR}.", abstract = "The proof of Lemma 3.4 in [F] relies on the incorrect equality $\mu_j (AB) = \mu_j (BA)$ for singular values (for a counterexample, see [S, p. 4]). Thus, Theorem 3.1 as stated has not been proven. However, with minor changes, we can obtain a bound for the counting function in terms of the growth of the Fourier transform of $|V|$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Goulden:2001:ITF, author = "I. P. Goulden and D. M. Jackson and F. G. Latour", title = "Inequivalent Transitive Factorizations into Transpositions", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "758--779", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-031-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions. It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factorizations, where two factorizations are equivalent if they differ only by the interchange of adjacent factors that commute. We obtain an explicit and elegant result for the number of such factorizations of permutations with precisely two factors. The approach used is a combinatorial one that rests on two constructions. We believe that this approach, and the combinatorial primitives that have been developed for the ``cut and join'' analysis, will also assist with the general case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nicolaescu:2001:SWI, author = "Liviu I. Nicolaescu", title = "{Seiberg--Witten} Invariants of Lens Spaces", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "780--808", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-032-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We show that the Seiberg--Witten invariants of a lens space determine and are determined by its Casson-Walker invariant and its Reidemeister-Turaev torsion.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Robertson:2001:ATG, author = "Guyan Robertson and Tim Steger", title = "Asymptotic {$K$}-Theory for Groups Acting on {$\tA_2$} Buildings", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "809--833", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-033-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\Gamma$ be a torsion free lattice in $G=\PGL(3, \mathbb{F})$ where $\mathbb{F}$ is a nonarchimedean local field. Then $\Gamma$ acts freely on the affine Bruhat-Tits building $\mathcal{B}$ of $G$ and there is an induced action on the boundary $\Omega$ of $\mathcal{B}$. The crossed product $C^*$-algebra $\mathcal{A}(\Gamma)=C(\Omega) \rtimes \Gamma$ depends only on $\Gamma$ and is classified by its $K$-theory. This article shows how to compute the $K$-theory of $\mathcal{A}(\Gamma)$ and of the larger class of rank two Cuntz-Krieger algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Veys:2001:ZFK, author = "Willem Veys", title = "Zeta Functions and `Kontsevich Invariants' on Singular Varieties", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "834--865", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-034-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $X$ be a nonsingular algebraic variety in characteristic zero. To an effective divisor on $X$ Kontsevich has associated a certain motivic integral, living in a completion of the Grothendieck ring of algebraic varieties. He used this invariant to show that birational (smooth, projective) Calabi--Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the invariant {\em motivic (Igusa) zeta function}, associated to a regular function on $X$, which specializes to both the classical $p$-adic Igusa zeta function and the topological zeta function, and also to Kontsevich's invariant. This paper treats a generalization to singular varieties. Batyrev already considered such a `Kontsevich invariant' for log terminal varieties (on the level of Hodge polynomials of varieties instead of in the Grothendieck ring), and previously we introduced a motivic zeta function on normal surface germs. Here on any $\bbQ$-Gorenstein variety $X$ we associate a motivic zeta function and a `Kontsevich invariant' to effective $\bbQ$-Cartier divisors on $X$ whose support contains the singular locus of $X$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yang:2001:IPP, author = "Yifan Yang", title = "Inverse Problems for Partition Functions", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "866--896", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-035-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $p_w(n)$ be the weighted partition function defined by the generating function $\sum^\infty_{n=0}p_w(n)x^n=\prod^\infty_{m=1} (1-x^m)^{-w(m)}$, where $w(m)$ is a non-negative arithmetic function. Let $P_w(u)=\sum_{n\le u}p_w(n)$ and $N_w(u)=\sum_{n\le u}w(n)$ be the summatory functions for $p_w(n)$ and $w(n)$, respectively. Generalizing results of G. A. Freiman and E. E. Kohlbecker, we show that, for a large class of functions $\Phi(u)$ and $\lambda(u)$, an estimate for $P_w(u)$ of the form $\log P_w(u)=\Phi(u)\bigl\{1+O(1/\lambda(u)\bigr)\bigr\}$ $(u\to\infty)$ implies an estimate for $N_w(u)$ of the form $N_w(u)=\Phi^\ast(u)\bigl\{1+O\bigl(1/\log\lambda(u)\bigr)\bigr\}$ $(u\to\infty)$ with a suitable function $\Phi^\ast(u)$ defined in terms of $\Phi(u)$. We apply this result and related results to obtain characterizations of the Riemann Hypothesis and the Generalized Riemann Hypothesis in terms of the asymptotic behavior of certain weighted partition functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bennett:2001:SEE, author = "Michael A. Bennett", title = "On Some Exponential Equations of {S. S. Pillai}", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "897--922", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-036-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we establish a number of theorems on the classic Diophantine equation of S. S. Pillai, $a^x-b^y=c$, where $a$, $b$ and $c$ are given nonzero integers with $a,b \geq 2$. In particular, we obtain the sharp result that there are at most two solutions in positive integers $x$ and $y$ and deduce a variety of explicit conditions under which there exists at most a single such solution. These improve or generalize prior work of Le, Leveque, Pillai, Scott and Terai. The main tools used include lower bounds for linear forms in the logarithms of (two) algebraic numbers and various elementary arguments.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Geramita:2001:DHF, author = "Anthony V. Geramita and Tadahito Harima and Yong Su Shin", title = "Decompositions of the {Hilbert} Function of a Set of Points in {$\P^n$}", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "923--943", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-037-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\H$ be the Hilbert function of some set of distinct points in $\P^n$ and let $\alpha = \alpha (\H)$ be the least degree of a hypersurface of $\P^n$ containing these points. Write $\alpha = d_s + d_{s-1} + \cdots + d_1$ (where $d_i > 0$). We canonically decompose $\H$ into $s$ other Hilbert functions $\H \leftrightarrow (\H_s^\prime, \dots, \H_1^\prime)$ and show how to find sets of distinct points $\Y_s, \dots, \Y_1$, lying on reduced hypersurfaces of degrees $d_s, \dots, d_1$ (respectively) such that the Hilbert function of $\Y_i$ is $\H_i^\prime$ and the Hilbert function of $\Y = \bigcup_{i=1}^s \Y_i$ is $\H$. Some extremal properties of this canonical decomposition are also explored.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ludwig:2001:RIB, author = "J. Ludwig and C. Molitor-Braun", title = "Repr{\'e}sentations irr{\'e}ductibles born{\'e}es des groupes de {Lie} exponentiels. ({French}) [{Bounded} irreducible representations of exponential {Lie} groups]", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "944--978", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-038-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations $(T, \calU)$ of $G$ on a Banach space $\calU$ by giving a $G$-orbit in $\frn^*$ ($\frn$ being the nilradical of $\frg$), a topologically irreducible representation of $L^1(\RR^n, \o)$, for a certain weight $\o$ and a certain $n \in \NN$, and a topologically simple extension norm. If $G$ is not symmetric, \ie, if the weight $\o$ is exponential, we get a new type of representations which are fundamentally different from the induced representations. Soit $G$ un groupe de Lie r{\'e}soluble exponentiel. Nous caract{\'e}risons toutes les repr{\'e}sentations $(T, \calU)$ continues born{\'e}es topologiquement irr{\'e}ductibles de $G$ dans un espace de Banach $\calU$ {\`a} l'aide d'une $G$-orbite dans $\frn^*$ ($\frn$ {\'e}tant le radical nilpotent de $\frg$), d'une repr{\'e}sentation topologiquement irr{\'e}ductible de $L^1(\RR^n, \o)$, pour un certain poids $\o$ et un certain $n \in \NN$, d'une norme d'extension topologiquement simple. Si $G$ n'est pas sym{\'e}trique, c. {\`a} d. si le poids $\o$ est exponentiel, nous obtenons un nouveau type de repr{\'e}sentations qui sont fondamentalement diff{\'e}rentes des repr{\'e}sentations induites.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Nagisa:2001:RAC, author = "Masaru Nagisa and Hiroyuki Osaka and N. Christopher Phillips", title = "Ranks of Algebras of Continuous {$C^*$}-Algebra Valued Functions", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "979--1030", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-039-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove a number of results about the stable and particularly the real ranks of tensor products of \ca s under the assumption that one of the factors is commutative. In particular, we prove the following: {\raggedright \begin{enumerate}[(5)] \item[(1)] If $X$ is any locally compact $\sm$-compact Hausdorff space and $A$ is any \ca, then\break $\RR \bigl( C_0 (X) \otimes A \bigr) \leq \dim (X) + \RR(A)$. \item[(2)] If $X$ is any locally compact Hausdorff space and $A$ is any \pisca, then $\RR \bigl( C_0 (X) \otimes A \bigr) \leq 1$. \item[(3)] $\RR \bigl( C ([0,1]) \otimes A \bigr) \geq 1$ for any nonzero \ca\ $A$, and $\sr \bigl( C ([0,1]^2) \otimes A \bigr) \geq 2$ for any unital \ca\ $A$. \item[(4)] If $A$ is a unital \ca\ such that $\RR(A) = 0$, $\sr (A) = 1$, and $K_1 (A) = 0$, then\break $\sr \bigl( C ([0,1]) \otimes A \bigr) = 1$. \item[(5)] There is a simple separable unital nuclear \ca\ $A$ such that $\RR(A) = 1$ and\break $\sr \bigl( C ([0,1]) \otimes A \bigr) = 1$. \end{enumerate}}", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sampson:2001:CMP, author = "G. Sampson and P. Szeptycki", title = "The Complete {$(L^p, L^p)$} Mapping Properties of Some Oscillatory Integrals in Several Dimensions", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1031--1056", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-040-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that the operators $\int_ {\mathbb{R}_+^2} e^{ix^a \cdot y^b} \varphi (x,y) f(y)\, dy$ map $L^p(\mathbb{R}^2)$ into itself for $p \in J =\bigl[\frac{a_l+b_l}{a_l+(\frac{b_l r}{2})}, \frac{a_l+b_l} {a_l(1-\frac{r}{2})}\bigr]$ if $a_l,b_l\ge 1$ and $\varphi(x,y)=|x-y|^{-r}$, $0\le r < 2$, the result is sharp. Generalizations to dimensions $d > 2$ are indicated.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Varopoulos:2001:PTL, author = "N. Th. Varopoulos", title = "Potential Theory in {Lipschitz} Domains", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1057--1120", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-041-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove comparison theorems for the probability of life in a Lipschitz domain between Brownian motion and random walks. On donne des th{\'e}or{\`e}mes de comparaison pour la probabilit{\'e} de vie dans un domain Lipschitzien entre le Brownien et de marches al{\'e}atoires.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Athanasiadis:2001:MPZ, author = "Christos A. Athanasiadis and Francisco Santos", title = "Monotone Paths on Zonotopes and Oriented Matroids", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1121--1140", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-042-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Monotone paths on zonotopes and the natural generalization to maximal chains in the poset of topes of an oriented matroid or arrangement of pseudo-hyperplanes are studied with respect to a kind of local move, called polygon move or flip. It is proved that any monotone path on a $d$-dimensional zonotope with $n$ generators admits at least $\lceil 2n/(n-d+2) \rceil-1$ flips for all $n \ge d+2 \ge 4$ and that for any fixed value of $n-d$, this lower bound is sharp for infinitely many values of $n$. In particular, monotone paths on zonotopes which admit only three flips are constructed in each dimension $d \ge 3$. Furthermore, the previously known 2-connectivity of the graph of monotone paths on a polytope is extended to the 2-connectivity of the graph of maximal chains of topes of an oriented matroid. An application in the context of Coxeter groups of a result known to be valid for monotone paths on simple zonotopes is included.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bushnell:2001:CPT, author = "Colin J. Bushnell and Guy Henniart", title = "Sur le comportement, par torsion, des facteurs epsilon de paires. ({French}) [{Behavior}, by twisting, epsilon-pair factors]", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1141--1173", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-043-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soient $F$ un corps commutatif localement compact non archim{\'e}dien et $\psi$ un caract{\`e}re additif non trivial de $F$. Soient $n$ et $n'$ deux entiers distincts, sup{\'e}rieurs {\`a} $1$. Soient $\pi$ et $\pi'$ des repr{\'e}sentations irr{\'e}ductibles supercuspidales de $\GL_n(F)$, $\GL_{n'}(F)$ respectivement. Nous prouvons qu'il existe un {\'e}l{\'e}ment $c= c(\pi, \pi', \psi)$ de $F^\times$ tel que pour tout quasicaract{\`e}re mod{\'e}r{\'e} $\chi$ de $F^\times$ on ait $\varepsilon(\chi\pi\times \pi',s, \psi) = \chi(c)^{-1}\varepsilon(\pi\times\pi',s, \psi)$. Nous examinons aussi certains cas o{\`u} $n=n'$, $\pi'=\pi^\vee$. Les r{\'e}sultats obtenus forment une {\'e}tape vers une d{\'e}monstration de la conjecture de Langlands pour $F$, qui ne fasse pas appel {\`a} la g{\'e}om{\'e}trie des vari{\'e}t{\'e}s modulaires, de Shimura ou de Drinfeld. Let $F$ be a non-Archimedean local field, and $\psi$ a non-trivial additive character of $F$. Let $n$ and $n'$ be distinct positive integers. Let $\pi$, $\pi'$ be irreducible supercuspidal representations of $\GL_n(F)$, $\GL_{n'}(F)$ respectively. We prove that there is $c= c(\pi, \pi', \psi)\in F^\times$ such that for every tame quasicharacter $\chi$ of $F^\times$ we have $\varepsilon(\chi\pi\times \pi',s, \psi) = \chi(c)^{-1}\varepsilon(\pi\times\pi',s, \psi)$. We also treat some cases where $n=n'$ and $\pi'=\pi^\vee$. These results are steps towards a proof of the Langlands conjecture for $F$, which would not use the geometry of modular---Shimura or Drinfeld---varieties.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Loewen:2001:GVP, author = "Philip D. Loewen and Xianfu Wang", title = "A Generalized Variational Principle", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1174--1193", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-044-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove a strong variant of the Borwein-Preiss variational principle, and show that on Asplund spaces, Stegall's variational principle follows from it via a generalized Smulyan test. Applications are discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Louboutin:2001:EUB, author = "St{\'e}phane Louboutin", title = "Explicit Upper Bounds for Residues of {Dedekind} Zeta Functions and Values of {$L$}-Functions at $s = 1$, and Explicit Lower Bounds for Relative Class Numbers of {$\CM$}-Fields", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1194--1222", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-045-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at $s=1$ of $L$-series associated with primitive characters on ray class groups of number fields. To make it quite clear to the reader how useful such bounds are when dealing with class number problems for $\CM$-fields, we deduce an upper bound for the root discriminants of the normal $\CM$-fields with (relative) class number one.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mygind:2001:CCS, author = "Jesper Mygind", title = "Classification of Certain Simple {$C^*$}-Algebras with Torsion in {$K_1$}", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1223--1308", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-046-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We show that the Elliott invariant is a classifying invariant for the class of $C^*$-algebras that are simple unital infinite dimensional inductive limits of finite direct sums of building blocks of the form \{f \in C(\T) \otimes M_n : f(x_i) \in M_{d_i}, i = 1,2, \dots,N\}, where $x_1,x_2, \dots,x_N \in \T$, $d_1,d_2, \dots,d_N$ are integers dividing $n$, and $M_{d_i}$ is embedded unitally into $M_n$. Furthermore we prove existence and uniqueness theorems for $*$-homomorphisms between such algebras and we identify the range of the invariant.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Steer:2001:DHK, author = "Brian Steer and Andrew Wren", title = "The {Donaldson--Hitchin--Kobayashi} Correspondence for Parabolic Bundles over Orbifold Surfaces", journal = j-CAN-J-MATH, volume = "53", number = "??", pages = "1309--1339", month = "????", year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-047-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A theorem of Donaldson on the existence of Hermitian-Einstein metrics on stable holomorphic bundles over a compact K{\"a}hler surface is extended to bundles which are parabolic along an effective divisor with normal crossings. Orbifold methods, together with a suitable approximation theorem, are used following an approach successful for the case of Riemann surfaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2001:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2001 --- pour 2001", journal = j-CAN-J-MATH, volume = "53", number = "6", pages = "1340--1343", month = dec, year = "2001", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2001-048-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v53/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Alekseev:2002:QPM, author = "A. Alekseev and Y. Kosmann-Schwarzbach and E. Meinrenken", title = "Quasi-{Poisson} Manifolds", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "3--29", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-001-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in \wedge$^3$ {\bf g} associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Treloar:2002:SGP, author = "Thomas Treloar", title = "The Symplectic Geometry of Polygons in the $3$-Sphere", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "30--54", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-002-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the symplectic geometry of the moduli spaces $M_r=M_r(\s^3)$ of closed $n$-gons with fixed side-lengths in the $3$-sphere. We prove that these moduli spaces have symplectic structures obtained by reduction of the fusion product of $n$ conjugacy classes in $\SU(2)$ by the diagonal conjugation action of $\SU(2)$. Here the fusion product of $n$ conjugacy classes is a Hamiltonian quasi-Poisson $\SU(2)$-manifold in the sense of [AKSM]. An integrable Hamiltonian system is constructed on $M_r$ in which the Hamiltonian flows are given by bending polygons along a maximal collection of nonintersecting diagonals. Finally, we show the symplectic structure on $M_r$ relates to the symplectic structure obtained from gauge-theoretic description of $M_r$. The results of this paper are analogues for the $3$-sphere of results obtained for $M_r(\h^3)$, the moduli space of $n$-gons with fixed side-lengths in hyperbolic $3$-space [KMT], and for $M_r(\E^3)$, the moduli space of $n$-gons with fixed side-lengths in $\E^3$ [KM1].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ban:2002:MFQ, author = "Chunsheng Ban and Lee J. McEwan and Andr{\'a}s N{\'e}methi", title = "On the {Milnor} Fiber of a Quasi-ordinary Surface Singularity", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "55--70", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-003-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We verify a generalization of (3.3) from [Le73] proving that the homotopy type of the Milnor fiber of a reduced hypersurface singularity depends only on the embedded topological type of the singularity. In particular, using Zariski68, Lipman83, Oh93, Gau88] for irreducible quasi-ordinary germs, it depends only on the normalized distinguished pairs of the singularity. The main result of the paper provides an explicit formula for the Euler-characteristic of the Milnor fiber in the surface case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Choi:2002:SPS, author = "Kwok-Kwong Stephen Choi and Jianya Liu", title = "Small Prime Solutions of Quadratic Equations", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "71--91", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-004-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $b_1, \dots,b_5$ be non-zero integers and $n$ any integer. Suppose that $b_1 + \cdots + b_5 \equiv n \pmod{24}$ and $(b_i,b_j) = 1$ for $1 \leq i < j \leq 5$. In this paper we prove that \begin{enumerate}[(ii)] \item[(i)] if $b_j$ are not all of the same sign, then the above quadratic equation has prime solutions satisfying $p_j \ll \sqrt{|n|} + \max \{|b_j|\}^{20+\ve}$; and \item[(ii)] if all $b_j$ are positive and $n \gg \max \{|b_j|\}^{41+ \ve}$, then the quadratic equation $b_1 p_1^2 + \cdots + b_5 p_5^2 = n$ is soluble in primes $p_j$. \end{enumerate}", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mezo:2002:CGL, author = "Paul Mezo", title = "Comparisons of General Linear Groups and their Metaplectic Coverings {I}", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "92--137", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-005-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prepare for a comparison of global trace formulas of general linear groups and their metaplectic coverings. In particular, we generalize the local metaplectic correspondence of Flicker and Kazhdan and describe the terms expected to appear in the invariant trace formulas of the above covering groups. The conjectural trace formulas are then placed into a form suitable for comparison.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Razak:2002:CSS, author = "Shaloub Razak", title = "On the Classification of Simple Stably Projectionless {$\C^*$}-Algebras", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "138--224", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-006-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is shown that simple stably projectionless $\C^S*$-algebras which are inductive limits of certain specified building blocks with trivial $\K$-theory are classified by their cone of positive traces with distinguished subset. This is the first example of an isomorphism theorem verifying the conjecture of Elliott for a subclass of the stably projectionless algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Arslan:2002:SWF, author = "Bora Arslan and Alexander P. Goncharov and Mefharet Kocatepe", title = "Spaces of {Whitney} Functions on {Cantor}-Type Sets", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "225--238", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-007-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce the concept of logarithmic dimension of a compact set. In terms of this magnitude, the extension property and the diametral dimension of spaces $\calE(K)$ can be described for Cantor-type compact sets.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cartwright:2002:ESP, author = "Donald I. Cartwright and Tim Steger", title = "Elementary Symmetric Polynomials in Numbers of Modulus $1$", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "239--262", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-008-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We describe the set of numbers \sigma$_k$ (z$_1$, ...,z$_{n+1}$), where z$_1$, ..., z$_{n+1}$ are complex numbers of modulus 1 for which z$_1$ z$_2$ cdots z$_{n+1}$ =1, and \sigma$_k$ denotes the k-th elementary symmetric polynomial. Consequently, we give sharp constraints on the coefficients of a complex polynomial all of whose roots are of the same modulus. Another application is the calculation of the spectrum of certain adjacency operators arising naturally on a building of type {\tilde A}$_n$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chaudouard:2002:IOP, author = "Pierre-Henri Chaudouard", title = "Int{\'e}grales orbitales pond{\'e}r{\'e}es sur les alg{\`e}bres de {Lie}: le cas $p$-adique. ({French}) [{Weighted} orbital integrals on {Lie} algebras: the $p$-adic case]", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "263--302", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-009-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soit $G$ un groupe r{\'e}ductif connexe d{\'e}fini sur un corps $p$-adique $F$ et $\ggo$ son alg{\`e}bre de Lie. Les int{\'e}grales orbitales pond{\'e}r{\'e}es sur $\ggo(F)$ sont des distributions $J_M(X,f)$---$f$ est une fonction test---index{\'e}es par les sous-groupes de L{\'e}vi $M$ de $G$ et les {\'e}l{\'e}ments semi-simples r{\'e}guliers $X \in \mgo(F)\cap \ggo_{\reg}$. Leurs analogues sur $G$ sont les principales composantes du c{\^o}t{\'e} g{\'e}om{\'e}trique des formules des traces locale et globale d'Arthur. Si $M=G$, on retrouve les int{\'e}grales orbitales invariantes qui, vues comme fonction de $X$, sont born{\'e}es sur $\mgo(F)\cap \ggo_{\reg}$ : c'est un r{\'e}sultat bien connu de Harish-Chandra. Si $M \subsetneq G$, les int{\'e}grales orbitales pond{\'e}r{\'e}es explosent au voisinage des {\'e}l{\'e}ments singuliers. Nous construisons dans cet article de nouvelles int{\'e}grales orbitales pond{\'e}r{\'e}es $J_M^b(X,f)$, {\'e}gales {\`a} $J_M(X,f)$ {\`a} un terme correctif pr{\`e}s, qui tout en conservant les principales propri{\'e}t{\'e}s des pr{\'e}c{\'e}dentes (comportement par conjugaison, d{\'e}veloppement en germes, {\em etc.}) restent born{\'e}es quand $X$ parcourt $\mgo(F)\cap\ggo_{\reg}$. Nous montrons {\'e}galement que les int{\'e}grales orbitales pond{\'e}r{\'e}es globales, associ{\'e}es {\`a} des {\'e}l{\'e}ments semi-simples r{\'e}guliers, se d{\'e}composent en produits de ces nouvelles int{\'e}grales locales.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Ghahramani:2002:CFC, author = "Fereidoun Ghahramani and Sandy Grabiner", title = "Convergence Factors and Compactness in Weighted Convolution Algebras", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "303--323", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-010-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study convergence in weighted convolution algebras $L^1(\omega)$ on $R^+$, with the weights chosen such that the corresponding weighted space $M(\omega)$ of measures is also a Banach algebra and is the dual space of a natural related space of continuous functions. We determine convergence factor $\eta$ for which weak$^\ast$-convergence of $\{\lambda_n\}$ to $\lambda$ in $M(\omega)$ implies norm convergence of $\lambda_n \ast f$ to $\lambda \ast f$ in $L^1 (\omega\eta)$. We find necessary and sufficient conditions which depend on $\omega$ and $f$ and also find necessary and sufficient conditions for $\eta$ to be a convergence factor for all $L^1(\omega)$ and all $f$ in $L^1(\omega)$. We also give some applications to the structure of weighted convolution algebras. As a preliminary result we observe that $\eta$ is a convergence factor for $\omega$ and $f$ if and only if convolution by $f$ is a compact operator from $M(\omega)$ (or $L^1(\omega)$) to $L^1 (\omega\eta)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Graham:2002:PRU, author = "Ian Graham and Hidetaka Hamada and Gabriela Kohr", title = "Parametric Representation of Univalent Mappings in Several Complex Variables", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "324--351", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-011-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $B$ be the unit ball of $\bb{C}^n$ with respect to an arbitrary norm. We prove that the analog of the Carath{\'e}odory set, {\em i.e.} the set of normalized holomorphic mappings from $B$ into $\bb{C}^n$ of ``positive real part'', is compact. This leads to improvements in the existence theorems for the Loewner differential equation in several complex variables. We investigate a subset of the normalized biholomorphic mappings of $B$ which arises in the study of the Loewner equation, namely the set $S^0(B)$ of mappings which have parametric representation. For the case of the unit polydisc these mappings were studied by Poreda, and on the Euclidean unit ball they were studied by Kohr. As in Kohr's work, we consider subsets of $S^0(B)$ obtained by placing restrictions on the mapping from the Carath{\'e}odory set which occurs in the Loewner equation. We obtain growth and covering theorems for these subsets of $S^0(B)$ as well as coefficient estimates, and consider various examples. Also we shall see that in higher dimensions there exist mappings in $S(B)$ which can be imbedded in Loewner chains, but which do not have parametric representation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Haines:2002:CCS, author = "Thomas J. Haines", title = "On Connected Components of {Shimura} Varieties", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "352--395", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-012-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the cohomology of connected components of Shimura varieties $S_{K^p}$ coming from the group $\GSp_{2g}$, by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character $\olomega$ on the group of connected components of $S_{K^p}$ we define an operator $L(\omega)$ on the cohomology groups with compact supports $H^i_c (S_{K^p}, \olbbQ_\ell)$, and then we prove that the virtual trace of the composition of $L(\omega)$ with a Hecke operator $f$ away from $p$ and a sufficiently high power of a geometric Frobenius $\Phi^r_p$, can be expressed as a sum of $\omega$-{\em weighted} (twisted) orbital integrals (where $\omega$-{\em weighted} means that the orbital integrals and twisted orbital integrals occuring here each have a weighting factor coming from the character $\olomega$). As the crucial step, we define and study a new invariant $\alpha_1 (\gamma_0; \gamma, \delta)$ which is a refinement of the invariant $\alpha (\gamma_0; \gamma, \delta)$ defined by Kottwitz. This is done by using a theorem of Reimann and Zink.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lebel:2002:FSS, author = "Andr{\'e} Lebel", title = "Framed Stratified Sets in {Morse} Theory", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "396--416", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-013-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we present a smooth framework for some aspects of the ``geometry of CW complexes'', in the sense of Buoncristiano, Rourke and Sanderson \cite{[BRS]}. We then apply these ideas to Morse theory, in order to generalize results of Franks \cite{[F]} and Iriye-Kono \cite{[IK]}. More precisely, consider a Morse function $f$ on a closed manifold $M$. We investigate the relations between the attaching maps in a CW complex determined by $f$, and the moduli spaces of gradient flow lines of $f$, with respect to some Riemannian metric on $M$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wooley:2002:SES, author = "Trevor D. Wooley", title = "Slim Exceptional Sets for Sums of Cubes", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "417--448", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-014-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy--Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by $9$, and not exceeding $X$, that fail to have a representation as the sum of $7$ cubes of prime numbers, is $O(X^{23/36+\eps})$. For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is $O(X^{11/36+\eps})$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Akrout:2002:TVE, author = "H. Akrout", title = "Th{\'e}or{\`e}me de {Vorono{\'\i}} dans les espaces sym{\'e}triques. ({French}) [{Vorono{\'\i}} theorem in symmetric spaces]", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "449--467", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-015-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "On d{\'e}montre un th{\'e}or{\`e}me de Vorono{\"\i} (caract{\'e}risation des maxima locaux de l'invariant d'Hermite) pour les familles de r{\'e}seaux param{\'e}tr{\'e}es par les espaces sym{\'e}triques irr{\'e}ductibles non exceptionnels de type non compact. We prove a theorem of Vorono{\"\i} type (characterisation of local maxima of the Hermite invariant) for the lattices parametrized by irreducible nonexceptional symmetric spaces of noncompact type.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Boyd:2002:MMD, author = "David W. Boyd and Fernando Rodriguez-Villegas", title = "{Mahler}'s Measure and the Dilogarithm ({I})", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "468--492", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-016-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "An explicit formula is derived for the logarithmic Mahler measure $m(P)$ of $P(x,y) = p(x)y - q(x)$, where $p(x)$ and $q(x)$ are cyclotomic. This is used to find many examples of such polynomials for which $m(P)$ is rationally related to the Dedekind zeta value $\zeta_F (2)$ for certain quadratic and quartic fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Braden:2002:PSG, author = "Tom Braden", title = "Perverse Sheaves on {Grassmannians}", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "493--532", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-017-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We compute the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety $\Lambda$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Castelle:2002:AFP, author = "Nathalie Castelle", title = "Approximations fortes pour des processus bivari{\'e}s. ({French}) [{Strong} approximations for bivariate processes]", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "533--553", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-018-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Nous {\'e}tablissons un r{\'e}sultat d'approximation forte pour des processus bivari{\'e}s ayant une partie gaussienne et une partie empirique. Ce r{\'e}esultat apporte un nouveau point de vue sur deux th{\'e}or{\`e}mes hongrois bidimensionnels {\'e}tablis pr{\'e}c{\'e}demment, concernant l'approximation par un processus de Kiefer d'un processus empirique uniforme unidimensionnel et l'approximation par un pont brownien bidimensionnel d'un processus empirique uniforme bidimensionnel. Nous les enrichissons un peu et montrons que sous leur nouvelle forme ils ne sont que deux {\'e}nonc{\'e}s d'un m{\^e}me r{\'e}sultat. We establish a strong approximation result for bivariate processes containing a Gaussian part and an empirical part. This result leads to a new point of view on two Hungarian bidimensional theorems previously established, about the approximation of an unidimensional uniform empirical process by a Kiefer process and the approximation of a bidimensional uniform empirical process by a bidimensional Brownian bridge. We enrich them slightly and we prove that, under their new fashion, they are but two statements of the same result.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Hausen:2002:EES, author = "J{\"u}rgen Hausen", title = "Equivariant Embeddings into Smooth Toric Varieties", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "554--570", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-019-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojective $G$-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extends the concept of an equivariant affine cone over a projective $G$-variety to a more general framework.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2002:DPD, author = "Chi-Kwong Li and Yiu-Tung Poon", title = "Diagonals and Partial Diagonals of Sum of Matrices", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "571--594", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-020-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given a matrix $A$, let $\mathcal{O}(A)$ denote the orbit of $A$ under a certain group action such as (1) $U(m) \otimes U(n)$ acting on $m \times n$ complex matrices $A$ by $(U,V)*A = UAV^t$, (2) $O(m) \otimes O(n)$ or $\SO(m) \otimes \SO(n)$ acting on $m \times n$ real matrices $A$ by $(U,V)*A = UAV^t$, (3) $U(n)$ acting on $n \times n$ complex symmetric or skew-symmetric matrices $A$ by $U*A = UAU^t$, (4) $O(n)$ or $\SO(n)$ acting on $n \times n$ real symmetric or skew-symmetric matrices $A$ by $U*A = UAU^t$. Denote by \mathcal{O}(A_1, \dots,A_k) = \{X_1 + \cdots + X_k : X_i \in \mathcal{O}(A_i), i = 1, \dots,k\} the joint orbit of the matrices $A_1, \dots,A_k$. We study the set of diagonals or partial diagonals of matrices in $\mathcal{O}(A_1, \dots,A_k)$, i.e., the set of vectors $(d_1, \dots,d_r)$ whose entries lie in the $(1,j_1), \dots,(r,j_r)$ positions of a matrix in $\mathcal{O}(A_1, \dots,A_k)$ for some distinct column indices $j_1, \dots,j_r$. In many cases, complete description of these sets is given in terms of the inequalities involving the singular values of $A_1, \dots,A_k$. We also characterize those extreme matrices for which the equality cases hold. Furthermore, some convexity properties of the joint orbits are considered. These extend many classical results on matrix inequalities, and answer some questions by Miranda. Related results on the joint orbit $\mathcal{O}(A_1, \dots,A_k)$ of complex Hermitian matrices under the action of unitary similarities are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nahlus:2002:LAP, author = "Nazih Nahlus", title = "{Lie} Algebras of Pro-Affine Algebraic Groups", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "595--607", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-021-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed field $K$ of characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra $\mathcal{L}(G)$ of the pro-affine algebraic group $G$ over $K$, which is discrete in the finite-dimensional case and linearly compact in general. As an example, if $L$ is any sub Lie algebra of $\mathcal{L}(G)$, we show that the closure of $[L,L]$ in $\mathcal{L}(G)$ is algebraic in $\mathcal{L}(G)$. We also discuss the Hopf algebra of representative functions $H(L)$ of a residually finite dimensional Lie algebra $L$. As an example, we show that if $L$ is a sub Lie algebra of $\mathcal{L}(G)$ and $G$ is connected, then the canonical Hopf algebra morphism from $K[G]$ into $H(L)$ is injective if and only if $L$ is algebraically dense in $\mathcal{L}(G)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Stanley:2002:LSC, author = "Donald Stanley", title = "On the {Lusternik--Schnirelmann} Category of Maps", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "608--633", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-022-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give conditions which determine if $\cat$ of a map go up when extending over a cofibre. We apply this to reprove a result of Roitberg giving an example of a CW complex $Z$ such that $\cat(Z)=2$ but every skeleton of $Z$ is of category $1$. We also find conditions when $\cat (f\times g) < \cat(f) + \cat(g)$. We apply our result to show that under suitable conditions for rational maps $f$, $\mcat(f) < \cat(f)$ is equivalent to $\cat(f) = \cat (f\times \id_{S^n})$. Many examples with $\mcat(f) < \cat(f)$ satisfying our conditions are constructed. We also answer a question of Iwase by constructing $p$-local spaces $X$ such that $\cat (X\times S^1) = \cat(X) = 2$. In fact for our spaces and every $Y \not\simeq *$, $\cat (X\times Y) \leq \cat(Y) +1 < \cat(Y) + \cat(X)$. We show that this same $X$ has the property $\cat(X) = \cat (X\times X) = \cl (X\times X) = 2$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Weber:2002:FSW, author = "Eric Weber", title = "Frames and Single Wavelets for Unitary Groups", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "634--647", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-023-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider a unitary representation of a discrete countable abelian group on a separable Hilbert space which is associated to a cyclic generalized frame multiresolution analysis. We extend Robertson's theorem to apply to frames generated by the action of the group. Within this setup we use Stone's theorem and the theory of projection valued measures to analyze wandering frame collections. This yields a functional analytic method of constructing a wavelet from a generalized frame multi\-resolution analysis in terms of the frame scaling vectors. We then explicitly apply our results to the action of the integers given by translations on $L^2({\mathbb R})$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yuan:2002:RSP, author = "Wenjun Yuan and Yezhou Li", title = "Rational Solutions of {Painlev{\'e}} Equations", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "648--672", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-024-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Consider the sixth Painlev{\'e} equation (P$_6$) below where $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex parameters. We prove the necessary and sufficient conditions for the existence of rational solutions of equation (P$_6$) in term of special relations among the parameters. The number of distinct rational solutions in each case is exactly one or two or infinite. And each of them may be generated by means of transformation group found by Okamoto [7] and B{\"a}cklund transformations found by Fokas and Yortsos [4]. A list of rational solutions is included in the appendix. For the sake of completeness, we collected all the corresponding results of other five Painlev{\'e} equations (P$_1$)--(P$_5$) below, which have been investigated by many authors [1]--[7].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Asgari:2002:LFS, author = "Mahdi Asgari", title = "Local {$L$}-Functions for Split Spinor Groups", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "673--693", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-025-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the local L-functions for Levi subgroups in split spinor groups defined via the Langlands-Shahidi method and prove a conjecture on their holomorphy in a half plane. These results have been used in the work of Kim and Shahidi on the functorial product for GL$_2$ x GL$_3$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gabriel:2002:CAS, author = "Michael J. Gabriel", title = "{Cuntz} Algebra States Defined by Implementers of Endomorphisms of the {$\CAR$} Algebra", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "694--708", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-026-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate representations of the Cuntz algebra mathcal{O}$_2$ on antisymmetric Fock space F$_a$ (\mathcal{K}$_1$) defined by isometric implementers of certain quasi-free endomorphisms of the CAR algebra in pure quasi-free states $\varphi_{P_1}$. We pay corresponding to these representations and the Fock special attention to the vector states on mathcal{O}$_2$ vacuum, for which we obtain explicit formulae. Restricting these states to the gauge-invariant subalgebra mathcal{F}$_2$, we find that for natural choices of implementers, they are again pure quasi-free and are, in fact, essentially the states varphi$_{P 1}$ . We proceed to consider the case for an arbitrary pair of implementers, and deduce that these Cuntz algebra representations are irreducible, as are their restrictions to mathcal{F}$_2$. The endomorphisms of B ( F$_a$ (\mathcal{K}$_1$)) associated with these representations of mathcal{O}$_2$ are also considered.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ismail:2002:IMR, author = "Mourad E. H. Ismail and Dennis Stanton", title = "$q$-Integral and Moment Representations for $q$-Orthogonal Polynomials", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "709--735", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-027-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function mathcal{E}$_q$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kearnes:2002:CFS, author = "K. A. Kearnes and E. W. Kiss and {\'A}. Szendrei and R. D. Willard", title = "Chief Factor Sizes in Finitely Generated Varieties", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "736--756", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-028-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let mathbf{A} be a k-element algebra whose chief factor size is c. We show that if mathbf{B} is in the variety generated by mathbf{A}, then any abelian chief factor of mathbf{B} that is not strongly abelian has size at most c$^{k-1}$. This solves Problem 5 of $The Structure of Finite Algebras,$ by D. Hobby and R. McKenzie. We refine this bound to c in the situation where the variety generated by mathbf{A} omits type mathbf{1}. As a generalization, we bound the size of multitraces of types mathbf{1}, mathbf{2}, and mathbf{3} by extending coordinatization theory. Finally, we exhibit some examples of bad behavior, even in varieties satisfying a congruence identity.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Larose:2002:SPG, author = "Benoit Larose", title = "Strongly Projective Graphs", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "757--768", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-029-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce the notion of strongly projective graph, and characterise these graphs in terms of their neighbourhood poset. We describe certain exponential graphs associated to complete graphs and odd cycles. We extend and generalise a result of Greenwell and Lov{\'a}sz [6]: if a connected graph $G$ does not admit a homomorphism to $K$, where $K$ is an odd cycle or a complete graph on at least 3 vertices, then the graph $G x K^s$ admits, up to automorphisms of $K$, exactly $s$ homomorphisms to $K$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Miyazaki:2002:NOW, author = "Takuya Miyazaki", title = "Nilpotent Orbits and {Whittaker} Functions for Derived Functor Modules of {$\Sp(2, \mathbb{R})$}", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "769--794", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-030-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the moderate growth generalized Whittaker functions, associated to a unitary character $\psi$ of a unipotent subgroup, for the non-tempered cohomological representation of $G = \Sp(2,R)$. Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint $G$-orbit of $\psi$ in $\mathfrak{g}_{\mathbb {R}^\ast}$ and the asymptotic support of the cohomological representation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Moller:2002:STT, author = "R{\"o}gnvaldur G. M{\"o}ller", title = "Structure Theory of Totally Disconnected Locally Compact Groups via Graphs and Permutations", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "795--827", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-031-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Willis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Moriyama:2002:SFS, author = "Tomonori Moriyama", title = "Spherical Functions for the Semisimple Symmetric Pair {$\bigl( \Sp(2, \mathbb{R}), \SL(2, \mathbb{C}) \bigr)$}", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "828--896", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-032-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let pi be an irreducible generalized principal series representation of G = Sp(2, \mathbb{R}) induced from its Jacobi parabolic subgroup. We show that the space of algebraic intertwining operators from pi to the representation induced from an irreducible admissible representation of SL(2, \mathbb{C}) in G is at most one dimensional. Spherical functions in the title are the images of K-finite vectors by this intertwining operator. We obtain an integral expression of Mellin--Barnes type for the radial part of our spherical function.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ayuso:2002:VTF, author = "Pedro Fortuny Ayuso", title = "The Valuative Theory of Foliations", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "897--915", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-033-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper gives a characterization of valuations that follow the singular infinitely near points of plane vector fields, using the notion of L'H{\^o}pital valuation, which generalizes a well known classical condition. With that tool, we give a valuative description of vector fields with infinite solutions, singularities with rational quotient of eigenvalues in its linear part, and polynomial vector fields with transcendental solutions, among other results.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bastien:2002:CCM, author = "G. Bastien and M. Rogalski", title = "Convexit{\'e}, compl{\`e}te monotonie et in{\'e}galit{\'e}s sur les fonctions z{\^e}ta et gamma sur les fonctions des op{\'e}rateurs de {Baskakov} et sur des fonctions arithm{\'e}tiques. ({French}) [Convexity, complete monotonicity, and inequality for zeta functions and gamma functions of the {Baskakov} operators and for arithmetic functions]", journal = j-CAN-J-MATH, volume = "54", number = "5", pages = "916--944", month = oct, year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-034-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give optimal upper and lower bounds for the function $H(x,s)=\sum_{n\geq 1}\frac{1}{(x+n)^s}$ for $x\geq 0$ and $s > 1$. These bounds improve the standard inequalities with integrals. We deduce from them inequalities about Riemann's $\zeta$ function, and we give a conjecture about the monotonicity of the function $s\mapsto[(s-1)\zeta(s)]^{\frac{1}{s-1}}$. Some applications concern the convexity of functions related to Euler's $\Gamma$ function and optimal majorization of elementary functions of Baskakov's operators. Then, the result proved for the function $x\mapsto x^{-s}$ is extended to completely monotonic functions. This leads to easy evaluation of the order of the generating series of some arithmetical functions when $z$ tends to 1. The last part is concerned with the class of non negative decreasing convex functions on $]0,+\infty[$, integrable at infinity. Nous prouvons un encadrement optimal pour la quantit{\'e} $H(x,s)=\sum_{n\geq 1}\frac{1}{(x+n)^s}$ pour $x\geq 0$ et $s > 1$, qui am{\'e}liore l'encadrement standard par des int{\'e}grales. Cet encadrement entra{\^\i}ne des in{\'e}galit{\'e}s sur la fonction $\zeta$ de Riemann, et am{\`e}ne {\`a} conjecturer la monotonie de la fonction $s\mapsto[(s-1)\zeta(s)]^{\frac{1}{s-1}}$. On donne des applications {\`a} l'{\'e}tude de la convexit{\'e} de fonctions li{\'e}es {\`a} la fonction $\Gamma$ d'Euler et {\`a} la majoration optimale des fonctions {\'e}l{\'e}mentaires intervenant dans les op{\'e}rateurs de Baskakov. Puis, nous {\'e}tendons aux fonctions compl{\`e}tement monotones sur $]0,+\infty[$ les r{\'e}sultats {\'e}tablis pour la fonction $x\mapsto x^{-s}$, et nous en d{\'e}duisons des preuves {\'e}l{\'e}mentaires du comportement, quand $z$ tend vers $1$, des s{\'e}ries g{\'e}n{\'e}ratrices de certaines fonctions arithm{\'e}tiques. Enfin, nous prouvons qu'une partie du r{\'e}sultat se g{\'e}n{\'e}ralise {\`a} une classe de fonctions convexes positives d{\'e}croissantes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Boivin:2002:ACS, author = "Andr{\'e} Boivin and Paul M. Gauthier and Petr V. Paramonov", title = "Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "945--969", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-035-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given a homogeneous elliptic partial differential operator $L$ with constant complex coefficients and a class of functions (jet-distributions) which are defined on a (relatively) closed subset of a domain $\Omega$ in $\mathbf{R}^n$ and which belong locally to a Banach space $V$, we consider the problem of approximating in the norm of $V$ the functions in this class by ``analytic'' and ``meromorphic'' solutions of the equation $Lu=0$. We establish new Roth, Arakelyan (including tangential) and Carleman type theorems for a large class of Banach spaces $V$ and operators $L$. Important applications to boundary value problems of solutions of homogeneous elliptic partial differential equations are obtained, including the solution of a generalized Dirichlet problem.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cegarra:2002:GCG, author = "A. M. Cegarra and J. M. Garc{\'\i}a-Calcines and J. A. Ortega", title = "On Graded Categorical Groups and Equivariant Group Extensions", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "970--997", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-036-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this article we state and prove precise theorems on the homotopy classification of graded categorical groups and their homomorphisms. The results use equivariant group cohomology, and they are applied to show a treatment of the general equivariant group extension problem.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dimassi:2002:RSV, author = "Mouez Dimassi", title = "Resonances for Slowly Varying Perturbations of a Periodic {Schr{\"o}dinger} Operator", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "998--1037", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-037-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the resonances of the operator $P(h) = -\Delta_x + V(x) + \varphi(hx)$. Here $V$ is a periodic potential, $\varphi$ a decreasing perturbation and $h$ a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of $P_0 = -\Delta_x + V(x)$, and we give its asymptotic expansions in powers of $h^{\frac12}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gavrilov:2002:BLC, author = "Lubomir Gavrilov and Iliya D. Iliev", title = "Bifurcations of Limit Cycles From Infinity in Quadratic Systems", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1038--1064", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-038-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate the bifurcation of limit cycles in one-parameter unfoldings of quadractic differential systems in the plane having a degenerate critical point at infinity. It is shown that there are three types of quadratic systems possessing an elliptic critical point which bifurcates from infinity together with eventual limit cycles around it. We establish that these limit cycles can be studied by performing a degenerate transformation which brings the system to a small perturbation of certain well-known reversible systems having a center. The corresponding displacement function is then expanded in a Puiseux series with respect to the small parameter and its coefficients are expressed in terms of Abelian integrals. Finally, we investigate in more detail four of the cases, among them the elliptic case (Bogdanov-Takens system) and the isochronous center $\mathcal{S}_3$. We show that in each of these cases the corresponding vector space of bifurcation functions has the Chebishev property: the number of the zeros of each function is less than the dimension of the vector space. To prove this we construct the bifurcation diagram of zeros of certain Abelian integrals in a complex domain.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hayashi:2002:LTB, author = "Nakao Hayashi and Pavel I. Naumkin", title = "Large Time Behavior for the Cubic Nonlinear {Schr{\"o}dinger} Equation", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1065--1085", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-039-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider the Cauchy problem for the cubic nonlinear Schr{\"o}dinger equation in one space dimension: iu$_t$ + frac{1}{2} u$_{xx}$ + \bar{u}$^3$ = 0, t \in {\bf R}, x \in {\bf R}, u(0,x) = u$_0$ (x), x \in {\bf R}. Cubic type nonlinearities in one space dimension heuristically appear to be critical for large time. We study the global existence and large time asymptotic behavior of solutions to the Cauchy problem (\ref{A}). We prove that if the initial data u$_0$ \in {\bf H}$^{1,0}$ \cap {\bf H}$^{0,1}$ are small and such that \sup$_{|\xi|\leq 1}$ |\arg mathcal{F} u$_0$ (\xi) - \frac{\pi n}{2}| < \frac{\pi}{8} for some n \in {\bf Z}, and \inf$_{|\xi|\leq 1}$ |\mathcal{F} u$_0$ (\xi)| > 0, then the solution has an additional logarithmic time-decay in the short range region $|x| \leq \sqrt{t}$. In the far region $|x| > \sqrt{t}$ the asymptotics have a quasi-linear character.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Polterovich:2002:CHT, author = "Iosif Polterovich", title = "Combinatorics of the Heat Trace on Spheres", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1086--1099", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-040-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed in [P].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wood:2002:OBF, author = "Peter J. Wood", title = "The Operator Biprojectivity of the {Fourier} Algebra", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1100--1120", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-041-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we investigate projectivity in the category of operator spaces. In particular, we show that the Fourier algebra of a locally compact group $G$ is operator biprojective if and only if $G$ is discrete.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bao:2002:FNE, author = "Jiguang Bao", title = "Fully Nonlinear Elliptic Equations on General Domains", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1121--1141", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-042-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "By means of the Pucci operator, we construct a function $u_0$, which plays an essential role in our considerations, and give the existence and regularity theorems for the bounded viscosity solutions of the generalized Dirichlet problems of second order fully nonlinear elliptic equations on the general bounded domains, which may be irregular. The approximation method, the accretive operator technique and the Caffarelli's perturbation theory are used.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Binding:2002:FDE, author = "Paul Binding and Branko 'Curgus", title = "Form Domains and Eigenfunction Expansions for Differential Equations with Eigenparameter Dependent Boundary Conditions", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1142--1164", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-043-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Form domains are characterized for regular $2n$-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first $n-1$ derivatives.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Blasco:2002:MVV, author = "Oscar Blasco and Jos{\'e} Luis Arregui", title = "Multipliers on Vector Valued {Bergman} Spaces", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1165--1186", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-044-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $X$ be a complex Banach space and let $B_p(X)$ denote the vector-valued Bergman space on the unit disc for $1\le p < \infty$. A sequence $(T_n)_n$ of bounded operators between two Banach spaces $X$ and $Y$ defines a multiplier between $B_p(X)$ and $B_q(Y)$ (resp.\ $B_p(X)$ and $\ell_q(Y)$) if for any function $f(z) = \sum_{n=0}^\infty x_n z^n$ in $B_p(X)$ we have that $g(z) = \sum_{n=0}^\infty T_n (x_n) z^n$ belongs to $B_q(Y)$ (resp.\ $\bigl( T_n (x_n) \bigr)_n \in \ell_q(Y)$). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces $X$ and $Y$. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in $B_p(X)$ are introduced.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cobo:2002:IMR, author = "Milton Cobo and Carlos Gutierrez and Jaume Llibre", title = "On the Injectivity of {$C^1$} Maps of the Real Plane", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1187--1201", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-045-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $X\colon\mathbb{R}^2\to\mathbb{R}^2$ be a $C^1$ map. Denote by $\Spec(X)$ the set of (complex) eigenvalues of $\DX_p$ when $p$ varies in $\mathbb{R}^2$. If there exists $\epsilon > 0$ such that $\Spec(X)\cap(-\epsilon, \epsilon)=\emptyset$, then $X$ is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fernandez:2002:OGR, author = "J. Fern{\'a}ndez and J-C. Lario and A. Rio", title = "Octahedral {Galois} Representations Arising From {$\mathbf{Q}$}-Curves of Degree $2$", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1202--1228", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-046-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Generically, one can attach to a {\bf Q} -curve $C$ octahedral representations $\rho\colon\Gal(\bar{\mathbf{Q}}/\mathbf{Q})\rightarrow\GL_2(\bar\mathbf{F}_3)$ coming from the Galois action on the $3$-torsion of those abelian varieties of $\GL_2$-type whose building block is $C$. When $C$ is defined over a quadratic field and has an isogeny of degree $2$ to its Galois conjugate, there exist such representations $\rho$ having image into $\GL_2(\mathbf{F}_9)$. Going the other way, we can ask which $\mod 3$ octahedral representations $\rho$ of $\Gal(\bar\mathbf{Q}/\mathbf{Q})$ arise from {\bf Q} -curves in the above sense. We characterize those arising from quadratic {\bf Q} -curves of degree $2$. The approach makes use of Galois embedding techniques in $\GL_2(\mathbf{F}_9)$, and the characterization can be given in terms of a quartic polynomial defining the $\mathcal{S}_4$-extension of $\mathbf{Q}$ corresponding to the projective representation $\bar{\rho}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gow:2002:WCU, author = "Roderick Gow and Fernando Szechtman", title = "The {Weil} Character of the Unitary Group Associated to a Finite Local Ring", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1229--1253", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-047-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\mathbf{R}/R$ be a quadratic extension of finite, commutative, local and principal rings of odd characteristic. Denote by $\mathbf{U}_n (\mathbf{R})$ the unitary group of rank $n$ associated to $\mathbf{R}/R$. The Weil representation of $\mathbf{U}_n (\mathbf{R})$ is defined and its character is explicitly computed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Isaev:2002:EAU, author = "A. V. Isaev and N. G. Kruzhilin", title = "Effective Actions of the Unitary Group on Complex Manifolds", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1254--1279", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-048-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We classify all connected $n$-dimensional complex manifolds admitting effective actions of the unitary group $U_n$ by biholomorphic transformations. One consequence of this classification is a characterization of $\CC^n$ by its automorphism group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Skrzypczak:2002:BSH, author = "Leszek Skrzypczak", title = "{Besov} Spaces and {Hausdorff} Dimension For Some {Carnot--Carath{\'e}odory} Metric Spaces", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1280--1304", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-049-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We regard a system of left invariant vector fields $\mathcal{X}=\{X_1, \dots,X_k\}$ satisfying the H{\"o}rmander condition and the related Carnot-Carath{\'e}odory metric on a unimodular Lie group $G$. We define Besov spaces corresponding to the sub-Laplacian $\Delta=\sum X_i^2$ both with positive and negative smoothness. The atomic decomposition of the spaces is given. In consequence we get the distributional characterization of the Hausdorff dimension of Borel subsets with the Haar measure zero.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Vulakh:2002:CFA, author = "L. Ya. Vulakh", title = "Continued Fractions Associated with {$\SL_3 (\mathbf{Z})$} and Units in Complex Cubic Fields", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1305--1318", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-050-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Continued fractions associated with GL$_3$ ( {\bf Z}) are introduced and applied to find fundamental units in a two-parameter family of complex cubic fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yekutieli:2002:CHC, author = "Amnon Yekutieli", title = "The Continuous {Hochschild} Cochain Complex of a Scheme", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1319--1337", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-051-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $X$ be a separated finite type scheme over a noetherian base ring $\mathbb{K}$. There is a complex $\widehat{\mathcal{C}}^{\cdot} (X)$ of topological $\mathcal{O}_X$-modules, called the complete Hochschild chain complex of $X$. To any $\mathcal{O}_X$-module $\mathcal{M}$---not necessarily quasi-coherent---we assign the complex $\mathcal{H}om^{\cont}_ {\mathcal{O}_X} \bigl( \widehat{\mathcal{C}}^{\cdot} (X), \mathcal{M} \bigr)$ of continuous Hochschild cochains with values in $\mathcal{M}$. Our first main result is that when $X$ is smooth over $\mathbb{K}$ there is a functorial isomorphism \mathcal{H}om^{\cont}_ {\mathcal{O}_X} \bigl( \widehat{\mathcal{C}}^{\cdot} (X), \mathcal{M} \bigr) \cong \R \mathcal{H}om_ {\mathcal{O}_ {X^2}} (\mathcal{O}_X, \mathcal{M}) in the derived category $\mathsf{D} (\Mod \mathcal{O}_ {X^2})$, where $X^2 := X \times_ {\mathbb{K}} X$. The second main result is that if $X$ is smooth of relative dimension $n$ and $n!$ is invertible in $\mathbb{K}$, then the standard maps $\pi \colon \widehat{\mathcal{C}}^{-q} (X) \to \Omega^q_ {X/ \mathbb{K}}$ induce a quasi-isomorphism \mathcal{H}om_ {\mathcal{O}_X} \Bigl( \bigoplus_q \Omega^q_ {X/ \mathbb{K}} [q], \mathcal{M} \Bigr) \to \mathcal{H}om^{\cont}_ {\mathcal{O}_X} \bigl( \widehat{\mathcal{C}}^{\cdot} (X), \mathcal{M} \bigr). When $\mathcal{M} = \mathcal{O}_X$ this is the quasi-isomorphism underlying the Kontsevich Formality Theorem. Combining the two results above we deduce a decomposition of the global Hochschild cohomology", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2002:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2002 --- pour 2002", journal = j-CAN-J-MATH, volume = "54", number = "??", pages = "1338--1342", month = "????", year = "2002", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2002-052-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:10 MDT 2011", bibsource = "http://cms.math.ca/cjm/v54/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baake:2003:ESM, author = "Michael Baake and Ellen Baake", title = "An Exactly Solved Model for Mutation, Recombination and Selection", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "3--41", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-001-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See erratum \cite{Baake:2008:EES}.", abstract = "It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from. Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of M{\"o}bius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Benanti:2003:SVG, author = "Francesca Benanti and Onofrio M. {Di Vincenzo} and Vincenzo Nardozza", title = "$ * $-Subvarieties of the Variety Generated by {$\bigl( {M_2(\mathbb{K})}, t \bigr)$}", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "42--63", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-002-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let {\bf K} be a field of characteristic zero, and *=t the transpose involution for the matrix algebra M$_2$ ( {\bf K}). Let \mathfrak{U} be a proper subvariety of the variety of algebras with involution generated by ( M$_2$ ( {\bf K}),*). We define two sequences of algebras with involution mathcal{R}$_p$, mathcal{S}$_q$, where p,q \in {\bf N}. Then we show that T$_*$ (\mathfrak{U}) and T$_*$ (\mathcal{R}$_p$ \oplus mathcal{S}$_q$) are *-asymptotically equivalent for suitable p,q.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Braun:2003:HOT, author = "R{\"u}diger W. Braun and Reinhold Meise and B. A. Taylor", title = "Higher Order Tangents to Analytic Varieties along Curves", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "64--90", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-003-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let V be an analytic variety in some open set in {\bf C}$^n$ which contains the origin and which is purely k-dimensional. For a curve \gamma in {\bf C}$^n$, defined by a convergent Puiseux series and satisfying \gamma(0) = 0, and $d \ge 1$, define V$_t$ := t$^{-d}$ ( V - \gamma(t)). Then the currents defined by V$_t$ converge to a limit current T$_{\gamma,d}$ [V] as t tends to zero. T$_{\gamma,d}$ [V] is either zero or its support is an algebraic variety of pure dimension k in {\bf C}$^n$. Properties of such limit currents and examples are presented. These results will be applied in a forthcoming paper to derive necessary conditions for varieties satisfying the local Phragm{\'e}n-Lindel{\"o}f condition that was used by H{\"o}rmander to characterize the constant coefficient partial differential operators which act surjectively on the space of all real analytic functions on {\bf R}$^n$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Choi:2003:SCF, author = "Man-Duen Choi and Chi-Kwong Li and Yiu-Tung Poon", title = "Some Convexity Features Associated with Unitary Orbits", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "91--111", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-004-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let mathcal{H}$_n$ be the real linear space of n x n complex Hermitian matrices. The unitary (similarity) orbit mathcal{U} (C) of C \in mathcal{H}$_n$ is the collection of all matrices unitarily similar to C. We characterize those C \in mathcal{H}$_n$ such that every matrix in the convex hull of mathcal{U}(C) can be written as the average of two matrices in mathcal{U}(C). The result is used to study spectral properties of submatrices of matrices in mathcal{U}(C), the convexity of images of mathcal{U} (C) under linear transformations, and some related questions concerning the joint C-numerical range of Hermitian matrices. Analogous results on real symmetric matrices are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Shen:2003:FM, author = "Zhongmin Shen", title = "{Finsler} Metrics with {${\bf K} = 0$} and {${\bf S} = 0$}", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "112--132", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-005-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Shimada:2003:ZVK, author = "Ichiro Shimada", title = "On the Zariski-van {Kampen} Theorem", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "133--156", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-006-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let f \colon E \to B be a dominant morphism, where E and B are smooth irreducible complex quasi-projective varieties, and let F$_b$ be the general fiber of f. We present conditions under which the homomorphism pi$_1$ (F$_b$) \to pi$_1$ (E) induced by the inclusion is injective.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Shimada:2003:ZHS, author = "Ichiro Shimada", title = "{Zariski} Hyperplane Section Theorem for {Grassmannian} Varieties", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "157--180", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-007-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let phi \colon X \to M be a morphism from a smooth irreducible complex quasi-projective variety X to a Grassmannian variety M such that the image is of dimension \ge 2. Let D be a reduced hypersurface in M, and \gamma a general linear automorphism of M. We show that, under a certain differential-geometric condition on phi(X) and D, the fundamental group pi$_1$ ( (\gamma \circ phi)$^{-1}$ (M \setminus D)) is isomorphic to a central extension of pi$_1$ (M \setminus D) \times pi$_1$ (X) by the cokernel of pi$_2$ (phi) \colon pi$_2$ (X) \to pi$_2$ (M).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Theriault:2003:HDI, author = "Stephen D. Theriault", title = "Homotopy Decompositions Involving the Loops of Coassociative Co-{$H$} Spaces", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "181--203", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-008-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "James gave an integral homotopy decomposition of \Sigma \Omega Sigma X, Hilton-Milnor one for \Omega (Sigma X \vee Sigma Y), and Cohen-Wu gave p-local decompositions of \Omega Sigma X if X is a suspension. All are natural. Using idempotents and telescopes we show that the James and Hilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-H spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-H space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yan:2003:NCO, author = "Yaqiang Yan", title = "On the Nonsquare Constants of {Orlicz} Spaces with {Orlicz} Norm", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "204--224", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-009-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let l$^{Phi}$ and L$^{Phi}$ (\Omega) be the Orlicz sequence space and function space generated by N-function Phi(u) with Orlicz norm. We give equivalent expressions for the nonsquare constants C$_J$ (l$^{Phi}$), C$_J$ ( L$^{Phi}$ (\Omega)) in sense of James and C$_S$ (l$^{Phi}$), C$_S$ ( L$^{Phi}$ (\Omega)) in sense of Sch{\"a}ffer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces l$^{Phi}$ and L$^{Phi}$ (\Omega).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Banks:2003:SKS, author = "William D. Banks and Asma Harcharras and Igor E. Shparlinski", title = "Short {Kloosterman} Sums for Polynomials over Finite Fields", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "225--246", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-010-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring {\bf F}$_q$ [x]/M(x) for collections of polynomials either of the form f$^{-1}$ g$^{-1}$ or of the form f$^{-1}$ g$^{-1}$ +afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cushman:2003:DSO, author = "Richard Cushman and J{\k{e}}drzej {\'S}niatycki", title = "{``Differential Structure of Orbit Spaces''}: Erratum", journal = j-CAN-J-MATH, volume = "55", number = "2", pages = "247--247", month = apr, year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-011-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{Cushman:2001:DSO}.", abstract = "This note signals an error in the above paper by giving a counter-example.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dhillon:2003:GTT, author = "Ajneet Dhillon", title = "A Generalized {Torelli} Theorem", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "248--265", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-012-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given a smooth projective curve C of positive genus g, Torelli's theorem asserts that the pair ( J(C),W$^{g-1}$) determines C. We show that the theorem is true with W$^{g-1}$ replaced by W$^d$ for each d in the range 1 \le d \le g-1.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kogan:2003:TAM, author = "Irina A. Kogan", title = "Two Algorithms for a Moving Frame Construction", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "266--291", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-013-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The method of moving frames, introduced by Elie Cartan, is a powerful tool for the solution of various equivalence problems. The practical implementation of Cartan's method, however, remains challenging, despite its later significant development and generalization. This paper presents two new variations on the Fels and Olver algorithm, which under some conditions on the group action, simplify a moving frame construction. In addition, the first algorithm leads to a better understanding of invariant differential forms on the jet bundles, while the second expresses the differential invariants for the entire group in terms of the differential invariants of its subgroup.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pitman:2003:IDL, author = "Jim Pitman and Marc Yor", title = "Infinitely Divisible Laws Associated with Hyperbolic Functions", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "292--330", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-014-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The infinitely divisible distributions on {\bf R}$^+$ of random variables C$_t$, S$_t$ and T$_t$ with Laplace transforms (frac{1}{\cosh \sqrt{2\lambda}})$^t$, (frac{\sqrt{2\lambda}}{\sinh \sqrt{2\lambda}})$^t$, and (frac{\tanh \sqrt{2\lambda}}{\sqrt{2\lambda}})$^t$ respectively are characterized for various t > 0 in a number of different ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their L{\'e}vy measures, by recursions for their Mellin transforms, and by differential equations satisfied by their Laplace transforms. Some of these results are interpreted probabilistically via known appearances of these distributions for t=1 or 2 in the description of the laws of various functionals of Brownian motion and Bessel processes, such as the heights and lengths of excursions of a one-dimensional Brownian motion. The distributions of C$_1$ and S$_2$ are also known to appear in the Mellin representations of two important functions in analytic number theory, the Riemann zeta function and the Dirichlet L-function associated with the quadratic character modulo 4. Related families of infinitely divisible laws, including the \gamma, logistic and generalized hyperbolic secant distributions, are derived from S$_t$ and C$_t$ by operations such as Brownian subordination, exponential tilting, and weak limits, and characterized in various ways.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Savitt:2003:MNP, author = "David Savitt", title = "The Maximum Number of Points on a Curve of Genus $4$ over {$\mathbb{F}_8$} is $25$", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "331--352", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-015-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that the maximum number of rational points on a smooth, geometrically irreducible genus 4 curve over the field of 8 elements is 25. The body of the paper shows that 27 points is not possible by combining techniques from algebraic geometry with a computer verification. The appendix shows that 26 points is not possible by examining the zeta functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Silberger:2003:WEM, author = "Allan J. Silberger and Ernst-Wilhelm Zink", title = "Weak Explicit Matching for Level Zero Discrete Series of Unit Groups of $\mathfrak{p}$-Adic Simple Algebras", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "353--378", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-016-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let F be a $p$-adic local field and let A$_i^\times$ be the unit group of a central simple F-algebra A$_i$ of reduced degree n > 1 (i = 1, 2). Let mathcal{R}$^2$ (A$_i^\times$) denote the set of irreducible discrete series representations of A$_i^\times$. The {``Abstract Matching Theorem''} asserts the existence of a bijection, the {``Jacquet Langlands''} map {\cal JL}$_{A 2}$ A$_1$ : mathcal{R}$^2$ ( A$_1^\times$) \to mathcal{R}$^2$ ( A$_2^\times$) which, up to known sign, preserves character values for regular elliptic elements. This paper addresses the question of explicitly describing the map mathcal{J} mathcal{L}, but only for {``level zero''} representations. We prove that the restriction mathcal{J} mathcal{L}$_{A 2}$,A$_1$ : mathcal{R}$_0^2$ (A$_1^\times$) \to mathcal{R}$_0^2$ (A$_2^\times$) is a bijection of level zero discrete series (Proposition 3.2) and we give a parameterization of the set of unramified twist classes of level zero discrete series which does not depend upon the algebra A$_i$ and is invariant under mathcal{J} mathcal{L}$_{A 2}$,A$_1$ (Theorem 4.1).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Stessin:2003:GFH, author = "Michael Stessin and Kehe Zhu", title = "Generalized Factorization in {Hardy} Spaces and the Commutant of {Toeplitz} Operators", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "379--400", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-017-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Every classical inner function varphi in the unit disk gives rise to a certain factorization of functions in Hardy spaces. This factorization, which we call the generalized Riesz factorization, coincides with the classical Riesz factorization when varphi(z)=z. In this paper we prove several results about the generalized Riesz factorization, and we apply this factorization theory to obtain a new description of the commutant of analytic Toeplitz operators with inner symbols on a Hardy space. We also discuss several related issues in the context of the Bergman space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Varopoulos:2003:GEL, author = "N. Th. Varopoulos", title = "{Gaussian} Estimates in {Lipschitz} Domains", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "401--431", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-018-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give upper and lower Gaussian estimates for the diffusion kernel of a divergence and nondivergence form elliptic operator in a Lipschitz domain. On donne des estimations Gaussiennes pour le noyau d'une diffusion, r{\'e}versible ou pas, dans un domaine Lipschitzien.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zaharescu:2003:PCS, author = "Alexandru Zaharescu", title = "Pair Correlation of Squares in $p$-Adic Fields", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "432--448", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-019-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let p be an odd prime number, K a $p$-adic field of degree r over mathbf{Q}$_p$, O the ring of integers in K, B = {\beta$_1$,..., \beta$_r$} an integral basis of K over mathbf{Q}$_p$, u a unit in O and consider sets of the form mathcal{N}={n$_1$ \beta$_1$ + ... + n$_r$ \beta$_r$: 1 \leq n$_j$ \leq N$_j$, 1 \leq j \leq r}. We show under certain growth conditions that the pair correlation of {uz$^2$: z \in mathcal{N}} becomes Poissonian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Albeverio:2003:GSS, author = "Sergio Albeverio and Konstantin A. Makarov and Alexander K. Motovilov", title = "Graph Subspaces and the Spectral Shift Function", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "449--503", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-020-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2003:COR, author = "Jiecheng Chen and Dashan Fan and Yiming Ying", title = "Certain Operators with Rough Singular Kernels", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "504--532", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-021-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the singular integral operator $T$_{\Omega, \alpha}$ f$ ( $x$) $= p.v. \int$_{R$^n$}$ b$ (| $y$ |) $\Omega$ ( $y'$) | $y$ | $$^{-n- \alpha}$ f$ ( $x-y$) $dy,$ defined on all test functions $f$, where $b$ is a bounded function, $\alpha \geq$ 0, $\Omega(y')$ is an integrable function on the unit sphere S$^{n- 1}$ satisfying certain cancellation conditions. We prove that, for 1 $ < p < \infty$, $T$_{\Omega, \alpha}$$ extends bounded operator from the Sobolev space $L$^p_{\alpha}$$ to the Lebesgue space $L^p$ with $\Omega$ being a distribution in the Hardy space H$^q$ (S$^{n- 1}$) with $q=$ ( $n-$ 1)/( $n-$ 1 $+ \alpha$). The result extends some known results on the singular integral operators. As applications, we obtain the boundedness for $T$_{\Omega, \alpha}$$ on the Hardy spaces, as well as the boundedness for the truncated maximal operator T$^*_{\Omega,m}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Edo:2003:AME, author = "Eric Edo", title = "Automorphismes mod{\'e}r{\'e}s de l'espace affine. ({French}) [{Moderate} automorphisms of affine space]", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "533--560", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-022-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Le probl{\`e}me de Jung-Nagata ( $cf.$ [J], [N]) consiste {\`a} savoir s'il existe des automorphismes de k[x,y,z] qui ne sont pas mod{\'e}r{\'e}s. Nous proposons une approche nouvelle de cette question, fond{\'e}e sur l'utilisation de la th{\'e}orie des automates et du polygone de Newton. Cette approche permet notamment de g{\'e}n{\'e}raliser de fa{\c{c}}on significative les r{\'e}sultats de [A]. The Jung-Nagata's problem ( $cf.$ [J], [N]) asks if there exists non-tame (or wild) automorphisms of k[x,y,z]. We give a new way to attack this question, based on the automata theory and the Newton polygon. This new approch allows us to generalize significantly the results of [A].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Laface:2003:QHL, author = "Antonio Laface and Luca Ugaglia", title = "Quasi-Homogeneous Linear Systems on {$\mathbb{P}^2$} with Base Points of Multiplicity $5$", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "561--575", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-023-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we consider linear systems of {\bf P}$^2$ with all but one of the base points of multiplicity 5. We give an explicit way to evaluate the dimensions of such systems.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lukashov:2003:AOE, author = "A. L. Lukashov and F. Peherstorfer", title = "Automorphic Orthogonal and Extremal Polynomials", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "576--608", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-024-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is well known that many polynomials which solve extremal problems on a single interval as the Chebyshev or the Bernstein--Szeg{\H{o}} polynomials can be represented by trigonometric functions and their inverses. On two intervals one has elliptic instead of trigonometric functions. In this paper we show that the counterparts of the Chebyshev and Bernstein--Szeg{\H{o}} polynomials for several intervals can be represented with the help of automorphic functions, so-called Schottky--Burnside functions. Based on this representation and using the Schottky--Burnside automorphic functions as a tool several extremal properties of such polynomials as orthogonality properties, extremal properties with respect to the maximum norm, behaviour of zeros and recurrence coefficients, etc., are derived.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Moraru:2003:ISA, author = "Ruxandra Moraru", title = "Integrable Systems Associated to a {Hopf} Surface", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "609--635", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-025-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A Hopf surface is the quotient of the complex surface {\bf C} $$^2$ \setminus$ {0} by an infinite cyclic group of dilations of {\bf C}$^2$. In this paper, we study the moduli spaces {$\cal M$} $$^n$$ of stable SL (2, {\bf C}) -bundles on a Hopf surface {$\cal H$}, from the point of view of symplectic geometry. An important point is that the surface {$\cal H$} is an elliptic fibration, which implies that a vector bundle on {$\cal H$} can be considered as a family of vector bundles over an elliptic curve. We define a map $G: {\cal M}^n \rightarrow {\bf P}^{2 n+ 1}$ that associates to every bundle on {$\cal H$} a divisor, called the graph of the bundle, which encodes the isomorphism class of the bundle over each elliptic curve. We then prove that the map $G$ is an algebraically completely integrable Hamiltonian system, with respect to a given Poisson structure on ${\cal M}^n$. We also give an explicit description of the fibres of the integrable system. This example is interesting for several reasons; in particular, since the Hopf surface is not K{\"a}hler, it is an elliptic fibration that does not admit a section.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Schwartzman:2003:HDA, author = "Sol Schwartzman", title = "Higher Dimensional Asymptotic Cycles", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "636--648", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-026-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given a $p$-dimensional oriented foliation of an $n$-dimensional compact manifold $M$^n$$ and a transversal invariant measure $tau$, Sullivan has defined an element of $H$_p$$ ( $M$^n$,R$). This generalized the notion of a $mu$-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure $mu$. In this one-dimensional case there was a natural 1-1 correspondence between transversal invariant measures $tau$ and invariant measures $mu$ when one had a smooth flow without stationary points. For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zucconi:2003:SIP, author = "Francesco Zucconi", title = "Surfaces with $p_{g} = q = 2$ and an Irrational Pencil", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "649--672", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-027-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We describe the irrational pencils on surfaces of general type with $p$_g$ =q=$ 2.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anderson:2003:NCE, author = "Greg W. Anderson and Yi Ouyang", title = "A Note on Cyclotomic {Euler} Systems and the Double Complex Method", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "673--692", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-028-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let {\bf F} be a finite real abelian extension of {\bf Q}. Let M be an odd positive integer. For every squarefree positive integer r the prime factors of which are congruent to 1 modulo M and split completely in {\bf F}, the corresponding Kolyvagin class kappa$_r$ \in {\bf F}$^x$ / {\bf F}$^{x M}$ satisfies a remarkable and crucial recursion which for each prime number ell dividing r determines the order of vanishing of kappa$_r$ at each place of {\bf F} above ell in terms of kappa$_{r / ell}$. In this note we give the recursion a new and universal interpretation with the help of the double complex method introduced by Anderson and further developed by Das and Ouyang. Namely, we show that the recursion satisfied by Kolyvagin classes is the specialization of a universal recursion independent of {\bf F} satisfied by universal Kolyvagin classes in the group cohomology of the universal ordinary distribution ${\`a} la$ Kubert tensored with {\bf Z} /M {\bf Z}. Further, we show by a method involving a variant of the diagonal shift operation introduced by Das that certain group cohomology classes belonging (up to sign) to a basis previously constructed by Ouyang also satisfy the universal recursion.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Borne:2003:FRR, author = "Niels Borne", title = "Une formule de {Riemann--Roch} {\'e}quivariante pour les courbes. ({French}) [{A} formula of {Riemann--Roch} for equivariant curves]", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "693--710", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-029-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soit G un groupe fini agissant sur une courbe alg{\'e}brique projective et lisse X sur un corps alg{\'e}briquement clos k. Dans cet article, on donne une formule de Riemann--Roch pour la caract{\'e}ristique d'Euler {\'e}quivariante d'un G-faisceau inversible $\mathcal{L}$, {\`a} valeurs dans l'anneau $R_k (G)$ des caract{\`e}res du groupe G. La formule donn{\'e}e a un bon comportement fonctoriel en ce sens qu'elle rel{\`e}ve la formule classique le long du morphisme $\dim \colon R_k (G) \to \mathbb{Z}$, et est valable m{\^e}me pour une action sauvage. En guise d'application, on montre comment calculer explicitement le caract{\`e}re de l'espace des sections globales d'une large classe de G-faisceaux inversibles, en s'attardant sur le cas particulier d{\'e}licat du faisceau des diff{\`e}rentielles sur la courbe.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Broughan:2003:ATR, author = "Kevin A. Broughan", title = "Adic Topologies for the Rational Integers", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "711--723", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-030-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A topology on \mathbb{Z}, which gives a nice proof that the set of prime integers is infinite, is characterised and examined. It is found to be homeomorphic to \mathbb{Q}, with a compact completion homeomorphic to the Cantor set. It has a natural place in a family of topologies on \mathbb{Z}, which includes the p-adics, and one in which the set of rational primes \mathbb{P} is dense. Examples from number theory are given, including the primes and squares, Fermat numbers, Fibonacci numbers and k-free numbers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cao:2003:SLP, author = "Xifang Cao and Qingkai Kong and Hongyou Wu and Anton Zettl", title = "{Sturm--Liouville} Problems Whose Leading Coefficient Function Changes Sign", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "724--749", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-031-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a given Sturm--Liouville equation whose leading coefficient function changes sign, we establish inequalities among the eigenvalues for any coupled self-adjoint boundary condition and those for two corresponding separated self-adjoint boundary conditions. By a recent result of Binding and Volkmer, the eigenvalues (unbounded from both below and above) for a separated self-adjoint boundary condition can be numbered in terms of the Pr{\"u}fer angle; and our inequalities can then be used to index the eigenvalues for any coupled self-adjoint boundary condition. Under this indexing scheme, we determine the discontinuities of each eigenvalue as a function on the space of such Sturm--Liouville problems, and its range as a function on the space of self-adjoint boundary conditions. We also relate this indexing scheme to the number of zeros of eigenfunctions. In addition, we characterize the discontinuities of each eigenvalue under a different indexing scheme.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gobel:2003:AFR, author = "R{\"u}diger G{\"o}bel and Saharon Shelah and Lutz Str{\"u}ngmann", title = "Almost-Free {$E$}-Rings of Cardinality $\aleph_1$", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "750--765", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-032-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "An E-ring is a unital ring R such that every endomorphism of the underlying abelian group R$^+$ is multiplication by some ring element. The existence of almost-free E-rings of cardinality greater than 2$^{aleph 0}$ is undecidable in \ZFC. While they exist in Gi{\"o}del's universe, they do not exist in other models of set theory. For a regular cardinal aleph$_1$ \leq \lambda \leq 2$^{aleph 0}$ we construct E-rings of cardinality \lambda in \ZFC which have aleph$_1$-free additive structure. For lambda = aleph$_1$ we therefore obtain the existence of almost-free E-rings of cardinality aleph$_1$ in ZFC.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kerler:2003:HTA, author = "Thomas Kerler", title = "Homology {TQFT}'s and the {Alexander--Reidemeister} Invariant of 3-Manifolds via {Hopf} Algebras and Skein Theory", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "766--821", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-033-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology of U(1)-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra mathcal{N} = \mathbb{Z}/2 \ltimes \bigwedge$^*$ \mathbb{R}$^2$ on the other side. We find that both TQFT's are \SL (2, \mathbb{R})-equivariant functors and, as such, are isomorphic. The \SL (2, \mathbb{R})-action in the Hennings construction comes from the natural action on \mathcal{N} and in the case of the Frohman-Nicas theory from the Hard-Lefschetz decomposition of the U(1)-moduli spaces given that they are naturally K{\"a}hler. The irreducible components of this TQFT, corresponding to simple representations of \SL(2, \mathbb{Z}) and \Sp(2g, \mathbb{Z}), thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg--Witten theories, Casson type theories for homology circles ${\`a} la$ Donaldson, higher rank gauge theories following Frohman and Nicas, and the \mathbb{Z}/p\mathbb{Z} reductions of Reshetikhin-Turaev theories over the cyclotomic integers \mathbb{Z} [\zeta$_p$ ]. We also conjecture that the Hennings TQFT for quantum-\mathfrak{sl}$_2$ is the product of the Reshetikhin-Turaev TQFT and such a homological TQFT.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kim:2003:OGP, author = "Djun Maximilian Kim and Dale Rolfsen", title = "An Ordering for Groups of Pure Braids and Fibre-Type Hyperplane Arrangements", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "822--838", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-034-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We define a total ordering of the pure braid groups which is invariant under multiplication on both sides. This ordering is natural in several respects. Moreover, it well-orders the pure braids which are positive in the sense of Garside. The ordering is defined using a combination of Artin's combing technique and the Magnus expansion of free groups, and is explicit and algorithmic. By contrast, the full braid groups (on 3 or more strings) can be ordered in such a way as to be invariant on one side or the other, but not both simultaneously. Finally, we remark that the same type of ordering can be applied to the fundamental groups of certain complex hyperplane arrangements, a direct generalization of the pure braid groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2003:CCT, author = "Min Ho Lee", title = "Cohomology of Complex Torus Bundles Associated to Cocycles", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "839--855", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-035-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Equivariant holomorphic maps of Hermitian symmetric domains into Siegel upper half spaces can be used to construct families of abelian varieties parametrized by locally symmetric spaces, which can be regarded as complex torus bundles over the parameter spaces. We extend the construction of such torus bundles using 2-cocycles of discrete subgroups of the semisimple Lie groups associated to the given symmetric domains and investigate some of their properties. In particular, we determine their cohomology along the fibers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Su:2003:PBS, author = "Yucai Su", title = "{Poisson} Brackets and Structure of Nongraded {Hamiltonian} {Lie} Algebras Related to Locally-Finite Derivations", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "856--896", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-036-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a ``sandwich'' method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson algebras are isomorphic. Furthermore, the derivation algebras and the second cohomology groups are determined.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Archinard:2003:HAV, author = "Nat{\'a}lia Archinard", title = "Hypergeometric {Abelian} Varieties", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "897--932", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-037-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we construct abelian varieties associated to Gauss' and Appell-Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, W{\"u}stholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Beineke:2003:RP, author = "Jennifer Beineke and Daniel Bump", title = "Renormalized Periods on {$\GL(3)$}", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "933--968", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-038-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A theory of renormalization of divergent integrals over torus periods on GL(3) is given, based on a relative truncation. It is shown that the renormalized periods of Eisenstein series have unexpected functional equations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Glockner:2003:LGM, author = "Helge Gl{\"o}ckner", title = "{Lie} Groups of Measurable Mappings", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "969--999", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-039-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We describe new construction principles for infinite-dimensional Lie groups. In particular, given any measure space (X, \Sigma, \mu) and (possibly infinite-dimensional) Lie group G, we construct a Lie group L$^{\infty}$ (X,G), which is a Fr{\'e}chet-Lie group if G is so. We also show that the weak direct product \prod$^*_{i\in I}$ G$_i$ of an arbitrary family (G$_i$)$_{i\in I}$ of Lie groups can be made a Lie group, modelled on the locally convex direct sum \bigoplus$_{i\in I}$ L(G$_i$).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Graczyk:2003:SCR, author = "P. Graczyk and P. Sawyer", title = "Some Convexity Results for the {Cartan} Decomposition", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1000--1018", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-040-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we consider the set \mathcal{S} = a(e$^X$ K e$^Y$) where a(g) is the abelian part in the Cartan decomposition of g. This is exactly the support of the measure intervening in the product formula for the spherical functions on symmetric spaces of noncompact type. We give a simple description of that support in the case of SL(3, {\bf F}) where {\bf F} = {\bf R}, {\bf C} or {\bf H}. In particular, we show that \mathcal{S} is convex. We also give an application of our result to the description of singular values of a product of two arbitrary matrices with prescribed singular values.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Handelman:2003:MEP, author = "David Handelman", title = "More Eventual Positivity for Analytic Functions", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1019--1079", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-041-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Eventual positivity problems for real convergent Maclaurin series lead to density questions for sets of harmonic functions. These are solved for large classes of series, and in so doing, asymptotic estimates are obtained for the values of the series near the radius of convergence and for the coefficients of convolution powers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kellerhals:2003:QSG, author = "Ruth Kellerhals", title = "Quaternions and Some Global Properties of Hyperbolic $5$-Manifolds", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1080--1099", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-042-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We provide an explicit thick and thin decomposition for oriented hyperbolic manifolds M of dimension 5. The result implies improved universal lower bounds for the volume vol$_5$ (M) and, for M compact, new estimates relating the injectivity radius and the diameter of M with vol$_5$ (M). The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group PS$_{\Delta}$ L (2, \mathbb{H}) of quaternionic 2 x 2-matrices with Dieudonn{\'e} determinant \Delta equal to 1 and isolation properties of PS$_{\Delta}$ L (2, \mathbb{H}).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Khesin:2003:PH, author = "Boris Khesin and Alexei Rosly", title = "Polar Homology", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1100--1120", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-043-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincar{\'e} residue on it. One can also define the corresponding analogues for the intersection and linking numbers of complex submanifolds, which have the properties similar to those of the corresponding topological notions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bettaieb:2003:CRT, author = "Karem Betta{\"\i}eb", title = "Classification des repr{\'e}sentations temp{\'e}r{\'e}es d'un groupe $p$-adique. ({French}) [{Classification} of representations of a temperate $p$-adic group]", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1121--1133", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-044-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soit $G$ le groupe des points d{\'e}finis sur un corps $p$-adique d'un groupe r{\'e}ductif connexe. A l'aide des caract{\`e}res virtuels supertemp{\'e}r{\'e}s de $G$, on prouve (conjectures de Clozel) que toute repr{\'e}sentation irr{\'e}ductible temp{\'e}r{\'e}e de $G$ est irr{\'e}ductiblement induite d'une essentielle d'un sous-groupe de L{\'e}vi de~ $G$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Casarino:2003:NCH, author = "Valentina Casarino", title = "Norms of Complex Harmonic Projection Operators", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1134--1154", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-045-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we estimate the $(L^p-L$^2$)$-norm of the complex harmonic projectors $\pi_{\ell\ell'}$, $1le ple 2$, uniformly with respect to the indexes $\ell, \ell'$. We provide sharp estimates both for the projectors $\pi_{\ell\ell'}$, when $\ell, \ell'$ belong to a proper angular sector in $\mathbb{N} \times \mathbb{N}$, and for the projectors $\pi_{\ell 0}$ and $\pi_{0 \ell}$. The proof is based on an extension of a complex interpolation argument by C.~Sogge. In the appendix, we prove in a direct way the uniform boundedness of a particular zonal kernel in the $L$^1$ $ norm on the unit sphere of $\mathbb{R}^{2n}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dokovic:2003:CON, author = "Dragomir {\v{Z}}. {\Dbar}okovi{\'c} and Michael Litvinov", title = "The Closure Ordering of Nilpotent Orbits of the Complex Symmetric Pair {$(\SO_{p + q}, \SO_p \times \SO_q)$}", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1155--1190", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-046-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The main problem that is solved in this paper has the following simple formulation (which is not used in its solution). The group $K = \mathrm{O}$_p$ ({\bf C}) \times \mathrm{O}$_q$ ({\bf C})$ acts on the space $M_{p,q}$ of $p\times q$ complex matrices by $(a,b) \cdot x = axb^{-1}$, and so does its identity component $K$^0$ = \SO$_p$ ({\bf C}) \times \SO$_q$ ({\bf C})$. A $K$-orbit (or $K$^0$ $-orbit) in $M_{p,q}$ is said to be nilpotent if its closure contains the zero matrix. The closure, $\overline{\mathcal{O}}$, of a nilpotent $K$-orbit (resp.\ $K$^0$ $-orbit) ${\mathcal{O}}$ in $M_{p,q}$ is a union of ${\mathcal{O}}$ and some nilpotent $K$-orbits (resp.\ $K$^0$ $-orbits) of smaller dimensions. The description of the closure of nilpotent $K$-orbits has been known for some time, but not so for the nilpotent $K$^0$ $-orbits. A conjecture describing the closure of nilpotent $K$^0$ $-orbits was proposed in \cite{DLS} and verified when $\min(p,q) le 7$. In this paper we prove the conjecture. The proof is based on a study of two prehomogeneous vector spaces attached to $\mathcal{O}$ and determination of the basic relative invariants of these spaces. The above problem is equivalent to the problem of describing the closure of nilpotent orbits in the real Lie algebra $\mathfrak{so} (p,q)$ under the adjoint action of the identity component of the real orthogonal group $\mathrm{O}(p,q)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Granville:2003:DMV, author = "Andrew Granville and K. Soundararajan", title = "Decay of Mean Values of Multiplicative Functions", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1191--1230", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-047-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For given multiplicative function $f$, with $|f(n)| \leq 1$ for all $n$, we are interested in how fast its mean value $(1/x) \sum_{n \leq x} f(n)$ converges. Hal{\'a}sz showed that this depends on the minimum $M$ (over $y\in \mathbb{R}$) of $\sum_{p \leq x} \bigl( 1 - \Re (f(p) p^{-iy}) \bigr) / p$, and subsequent authors gave the upper bound $ll (1+M) e^{-M}$. For many applications it is necessary to have explicit constants in this and various related bounds, and we provide these via our own variant of the Hal{\'a}sz-Montgomery lemma (in fact the constant we give is best possible up to a factor of 10). We also develop a new type of hybrid bound in terms of the location of the absolute value of $y$ that minimizes the sum above. As one application we give bounds for the least representatives of the cosets of the $k$-th powers mod~ $p$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Havin:2003:AMMa, author = "Victor Havin and Javad Mashreghi", title = "Admissible Majorants for Model Subspaces of {$H^2$}, Part {I}: Slow Winding of the Generating Inner Function", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1231--1263", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-048-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A model subspace $K_\Theta$ of the Hardy space $H$^2$ = H$^2$ (\mathbb{C} _+)$ for the upper half plane $\mathbb{C} _+$ is $H$^2$ (\mathbb{C} _+) \ominus \Theta H$^2$ (\mathbb{C} _+)$ where $\Theta$ is an inner function in $\mathbb{C} _+$. A function $\omega \colon \mathbb{R}\mapsto[0, \infty)$ is called {\em an admissible majorant\/} for $K_\Theta$ if there exists an $f \in K_\Theta$, $f \not\equiv 0$, $|f(x)| \leq \omega(x)$ almost everywhere on $\mathbb{R}$. For some (mainly meromorphic) $\Theta$'s some parts of $\Adm\Theta$ (the set of all admissible majorants for $K_\Theta$) are explicitly described. These descriptions depend on the rate of growth of $\arg \Theta$ along $\mathbb{R}$. This paper is about slowly growing arguments (slower than $x$). Our results exhibit the dependence of $\Adm B$ on the geometry of the zeros of the Blaschke product $B$. A complete description of $\Adm B$ is obtained for $B$ 's with purely imaginary ``vertical'') zeros. We show that in this case a unique minimal admissible majorant exists.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Havin:2003:AMMb, author = "Victor Havin and Javad Mashreghi", title = "Admissible Majorants for Model Subspaces of {$H^2$}, Part {II}: Fast Winding of the Generating Inner Function", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1264--1301", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-049-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper is a continuation of \cite{HM02I}. We consider the model subspaces $K_\Theta=H$^2$ \ominus\Theta H$^2$ $ of the Hardy space $H$^2$ $ generated by an inner function $\Theta$ in the upper half plane. Our main object is the class of admissible majorants for $K_\Theta$, denoted by $\Adm \Theta$ and consisting of all functions $\omega$ defined on $\mathbb{R}$ such that there exists an $f \ne 0$, $f \in K_\Theta$ satisfying $|f(x)| \leq \omega(x)$ almost everywhere on $\mathbb{R}$. Firstly, using some simple Hilbert transform techniques, we obtain a general multiplier theorem applicable to any $K_\Theta$ generated by a meromorphic inner function. In contrast with \cite{HM02I}, we consider the generating functions $\Theta$ such that the unit vector $\Theta(x)$ winds up fast as $x$ grows from $-\infty$ to $\infty$. In particular, we consider $\Theta=B$ where $B$ is a Blaschke product with {``horizontal''} zeros, {\em i.e.}, almost uniformly distributed in a strip parallel to and separated from $\mathbb{R}$. It is shown, among other things, that for any such $B$, any even $\omega$ decreasing on $(0, \infty)$ with a finite logarithmic integral is in $\Adm B$ (unlike the {``vertical''} case treated in \cite{HM02I}), thus generalizing (with a new proof) a classical result related to $\Adm\exp(i\sigma z)$, $\sigma > 0$. Some oscillating $\omega$'s in $\Adm B$ are also described. Our theme is related to the Beurling-Malliavin multiplier theorem devoted to $\Adm\exp(i\sigma z)$, $\sigma > 0$, and to de~Branges' space $\mathcal{H}(E)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Katsura:2003:ISC, author = "Takeshi Katsura", title = "The Ideal Structures of Crossed Products of {Cuntz} Algebras by Quasi-Free Actions of {Abelian} Groups", journal = j-CAN-J-MATH, volume = "55", number = "??", pages = "1302--1338", month = "????", year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-050-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A.~Kishimoto's result on the simplicity of such crossed products. We also give a necessary and sufficient condition that our algebras become primitive, and compute the Connes spectra and $K$-groups of our algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2003:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2003 --- pour 2003", journal = j-CAN-J-MATH, volume = "55", number = "6", pages = "1339--1342", month = dec, year = "2003", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2003-051-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v55/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Amini:2004:LCP, author = "Massoud Amini", title = "Locally Compact Pro-{$C^*$}-Algebras", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "3--22", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-001-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $X$ be a locally compact non-compact Hausdorff topological space. Consider the algebras $C(X), C$_b$ (X), C$_0$ (X)$, and $C$_{00}$ (X)$ of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions on $X$. Of these, the second and third are $C$^*$$-algebras, the fourth is a normed algebra, whereas the first is only a topological algebra (it is indeed a pro-$C$^*$$-algebra). The interesting fact about these algebras is that if one of them is given, the others can be obtained using functional analysis tools. For instance, given the $C$^*$$-algebra $C$_0$ (X)$, one can get the other three algebras by $C$_{00}$ (X)=K(C$_0$ (X)), C$_b$ (X)=M(C$_0$ (X)), C(X)= \Gamma(K(C$_0$ (X)))$, where the right hand sides are the Pedersen ideal, the multiplier algebra, and the unbounded multiplier algebra of the Pedersen ideal of $C$_0$ (X)$, respectively. In this article we consider the possibility of these transitions for general $C$^*$$-algebras. The difficult part is to start with a pro- $C$^*$$-algebra $A$ and to construct a $C$^*$$-algebra $A$_0$$ such that $A = \Gamma (K(A$_0$))$. The pro- $C$^*$$-algebras for which this is possible are called $locally compact$ and we have characterized them using a concept similar to that of an approximate identity.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bennett:2004:TDE, author = "Michael A. Bennett and Chris M. Skinner", title = "Ternary {Diophantine} Equations via {Galois} Representations and Modular Forms", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "23--54", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-002-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we develop techniques for solving ternary Diophantine equations of the shape $Ax$^n$ + By$^n$ = Cz$^2$$, based upon the theory of Galois representations and modular forms. We subsequently utilize these methods to completely solve such equations for various choices of the parameters $A$, $B$ and $C$. We conclude with an application of our results to certain classical polynomial-exponential equations, such as those of Ramanujan--Nagell type.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Harper:2004:E, author = "Malcolm Harper", title = "{{$\mathbb{Z}[\sqrt{14}]$}} is {Euclidean}", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "55--70", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-003-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We provide the first unconditional proof that the ring $\mathbb{Z} [\sqrt{14}]$ is a Euclidean domain. The proof is generalized to other real quadratic fields and to cyclotomic extensions of $\mathbb{Q}$. It is proved that if $K$ is a real quadratic field (modulo the existence of two special primes of $K$) or if $K$ is a cyclotomic extension of $\mathbb{Q}$ then: the ring of integers of $K$ is a Euclidean domain if and only if it is a principal ideal domain. The proof is a modification of the proof of a theorem of Clark and Murty giving a similar result when $K$ is a totally real extension of degree at least three. The main changes are a new Motzkin-type lemma and the addition of the large sieve to the argument. These changes allow application of a powerful theorem due to Bombieri, Friedlander and Iwaniec in order to obtain the result in the real quadratic case. The modification also allows the completion of the classification of cyclotomic extensions in terms of the Euclidean property.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Harper:2004:ERA, author = "Malcolm Harper and M. Ram Murty", title = "{Euclidean} Rings of Algebraic Integers", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "71--76", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-004-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a finite Galois extension of the field of rational numbers with unit rank greater than 3. We prove that the ring of integers of $K$ is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann hypothesis for Dedekind zeta functions. We now prove this unconditionally.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Holmes:2004:HDG, author = "Mark Holmes and Antal A. J{\'a}rai and Akira Sakai and Gordon Slade", title = "High-Dimensional Graphical Networks of Self-Avoiding Walks", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "77--114", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-005-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour for sufficiently spread-out networks on $\mathbb{Z}$^d$$ in dimensions $d > 4$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kenny:2004:EHD, author = "Robert Kenny", title = "Estimates of {Hausdorff} Dimension for the Non-Wandering Set of an Open Planar Billiard", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "115--133", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-006-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The billiard flow in the plane has a simple geometric definition; the movement along straight lines of points except where elastic reflections are made with the boundary of the billiard domain. We consider a class of open billiards, where the billiard domain is unbounded, and the boundary is that of a finite number of strictly convex obstacles. We estimate the Hausdorff dimension of the nonwandering set $M$_0$$ of the discrete time billiard ball map, which is known to be a Cantor set and the largest invariant set. Under certain conditions on the obstacles, we use a well-known coding of $M$_0$$ and estimates using convex fronts related to the derivative of the billiard ball map to estimate the Hausdorff dimension of local unstable sets. Consideration of the local product structure then yields the desired estimates, which provide asymptotic bounds on the Hausdorff dimension's convergence to zero as the obstacles are separated.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2004:LOM, author = "Chi-Kwong Li and Ahmed Ramzi Sourour", title = "Linear Operators on Matrix Algebras that Preserve the Numerical Range, Numerical Radius or the States", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "134--167", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-007-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Every norm nu on {\bf C}$^n$ induces two norm numerical ranges on the algebra $M$_n$$ of all $n x n$ complex matrices, the spatial numerical range W(A)= {x$^*$ Ay : x, y : {\bf C}$^n$, nu$^D$ (x) = nu(y) = x$^*$ y = 1}, where $nu$^D$$ is the norm dual to $nu$, and the algebra numerical range $V(A) = {f(A) : f : mathcal{S}},$ where $mathcal{S}$ is the set of states on the normed algebra $M$_n$$ under the operator norm induced by $nu$. For a symmetric norm $nu$, we identify all linear maps on $M$_n$$ that preserve either one of the two norm numerical ranges or the set of states or vector states. We also identify the numerical radius isometries, $i.e.$, linear maps that preserve the (one) numerical radius induced by either numerical range. In particular, it is shown that if $nu$ is not the $ell$_1$, ell$_2$$, or $ell$^\infty$$ norms, then the linear maps that preserve either numerical range or either set of states are {``inner''}, $i.e.$, of the form $A mapsto Q$^*$ AQ$, where $Q$ is a product of a diagonal unitary matrix and a permutation matrix and the numerical radius isometries are unimodular scalar multiples of such inner maps. For the $ell$_1$$ and the $ell$^\infty$$ norms, the results are quite different.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pogge:2004:CRS, author = "James Todd Pogge", title = "On a Certain Residual Spectrum of {$\Sp_8$}", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "168--193", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-008-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let G= {\bf Sp}$_{2n}$ be the symplectic group defined over a number field $F$. Let $\mathbb{A}$ be the ring of adeles. A fundamental problem in the theory of automorphic forms is to decompose the right regular representation of $G(\mathbb{A})$ acting on the Hilbert space $L$^2$ (G(F)setminus G(\mathbb{A}))$. Main contributions have been made by Langlands. He described, using his theory of Eisenstein series, an orthogonal decomposition of this space of the form: $L$_{dis}^2$ (G(F)setminus G(\mathbb{A})) = bigoplus$_{(M,pi)}$ L$_{dis}^2$ (G(F) setminus G(\mathbb{A}))$_{(M,pi)}$$, where $(M,pi)$ is a Levi subgroup with a cuspidal automorphic representation pi taken modulo conjugacy (Here we normalize $pi$ so that the action of the maximal split torus in the center of $G$ at the archimedean places is trivial.) and $L$_{dis}^2$ (G(F) setminus G(\mathbb{A}))$_{(M,pi)}$$ is a space of residues of Eisenstein series associated to $(M,pi)$. In this paper, we will completely determine the space $L$_{dis}^2$ (G(F) setminus G(\mathbb{A}))$_{(M,pi)}$$, when $M simeq GL$_2$ x GL$_2$$. This is the first result on the residual spectrum for non-maximal, non-Borel parabolic subgroups, other than $GL$_n$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Saikia:2004:SGE, author = "A. Saikia", title = "{Selmer} Groups of Elliptic Curves with Complex Multiplication", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "194--208", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-009-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Suppose $K$ is an imaginary quadratic field and $E$ is an elliptic curve over a number field $F$ with complex multiplication by the ring of integers in $K$. Let $p$ be a rational prime that splits as $\mathfrak{p}$_1$ \mathfrak{p}$_2$$ in $K$. Let $E$_{p$^n$}$$ denote the $p$^n$$-division points on $E$. Assume that $F(E$_{p$^n$}$)$ is abelian over $K$ for all $n geq 0$. This paper proves that the Pontrjagin dual of the $\mathfrak{p}$_1^\infty$$-Selmer group of $E$ over $F(E$_{p$^\infty$}$)$ is a finitely generated free $Lambda$-module, where Lambda is the Iwasawa algebra of Gal (F(E$_{p$^\infty$}$)/ F(E$_{\mathfrak{p} 1}^\infty$ \mathfrak{p}$_2$)). It also gives a simple formula for the rank of the Pontrjagin dual as a $Lambda$-module.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Schmuland:2004:CLT, author = "Byron Schmuland and Wei Sun", title = "A Central Limit Theorem and Law of the Iterated Logarithm for a Random Field with Exponential Decay of Correlations", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "209--224", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-010-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In [6], Walter Philipp wrote that {``... the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid.''} Many authors [1], [2], [4], [5], [9] have followed the plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables. We carry on this tradition by proving the law of the iterated logarithm for a random field whose correlations satisfy an exponential decay condition like the one obtained by Spohn [8] for certain Gibbs measures. These do not fall into the phi-mixing or strong mixing cases established in the literature, but are needed for our investigations [7] into diffusions on configuration space. The proofs are all obtained by patching together standard results from [5], [9] while keeping a careful eye on the correlations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Blower:2004:CUC, author = "Gordon Blower and Thomas Ransford", title = "Complex Uniform Convexity and {Riesz} Measure", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "225--245", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-011-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the distributional Laplacian gives a Riesz measure. This measure is calculated explicitly here for Lebesgue $L^p$ spaces and the von~Neumann-Schatten trace ideals. Banach spaces that are $q$-uniformly $PL$-convex in the sense of Davis, Garling and Tomczak-Jaegermann are characterized in terms of the mass distribution of this measure. This gives a new proof that the trace ideals $c^p$ are 2-uniformly $PL$-convex for $1 \leq p \leq 2$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bonnafe:2004:EUR, author = "C{\'e}dric Bonnaf{\'e}", title = "{\'E}l{\'e}ments unipotents r{\'e}guliers des sous-groupes de {Levi}. ({French}) [{Unipotent} regular elements of {Levi} subgroups ]", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "246--276", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-012-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate the structure of the centralizer of a regular unipotent element of a Levi subgroup of a reductive group. We also investigate the structure of the group of components of this centralizer in relation with the notion of cuspidal local system defined by Lusztig. We determine its unipotent radical, we prove that it admits a Levi complement, and we get some properties on its Weyl group. As an application, we prove some results which were announced in previous paper on regular unipotent elements. Nous {\'e}tudions la structure du centralisateur d'un {\'e}l{\'e}ment unipotent r{\'e}gulier d'un sous-groupe de Levi d'un groupe r{\'e}ductif, ainsi que la structure du groupe des composantes de ce centralisateur en relation avec la notion de syst{\`e}me local cuspidal d{\'e}finie par Lusztig. Nous d{\'e}terminons son radical unipotent, montrons l'existence d'un compl{\'e}ment de Levi et {\'e}tudions la structure de son groupe de Weyl. Comme application, nous d{\'e}montrons des r{\'e}sultats qui {\'e}taient annonc{\'e}s dans un pr{\'e}c{\'e}dent article de l'auteur sur les {\'e}l{\'e}ments unipotents r{\'e}guliers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Dostanic:2004:SPC, author = "Milutin R. Dostani{\'c}", title = "Spectral Properties of the Commutator of {Bergman}'s Projection and the Operator of Multiplication by an Analytic Function", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "277--292", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-013-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is shown that the singular values of the operator $aP - Pa$, where $P$ is Bergman's projection over a bounded domain $\Omega$ and $a$ is a function analytic on $bar{\Omega}$, detect the length of the boundary of $a(\Omega)$. Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Khomenko:2004:SMI, author = "Oleksandr Khomenko and Volodymyr Mazorchuk", title = "Structure of modules induced from simple modules with minimal annihilator", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "293--309", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-014-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to proper standard modules in some parabolic generalization of the Bernstein-Gelfand-Gelfand category $O$ and prove that the blocks of this parabolic category are equivalent to certain blocks of the category of Harish-Chandra bimodules. From this we derive, in particular, an irreducibility criterion for generalized Verma modules. We also compute the composition multiplicities of those simple subquotients, which correspond to the induction from simple modules whose annihilators are minimal primitive ideals.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Llibre:2004:GQD, author = "Jaume Llibre and Dana Schlomiuk", title = "The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "310--343", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-015-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this article we determine the global geometry of the planar quadratic differential systems with a weak focus of third order. This class plays a significant role in the context of Hilbert's 16-th problem. Indeed, all examples of quadratic differential systems with at least four limit cycles, were obtained by perturbing a system in this family. We use the algebro-geometric concepts of divisor and zero-cycle to encode global properties of the systems and to give structure to this class. We give a theorem of topological classification of such systems in terms of integer-valued affine invariants. According to the possible values taken by them in this family we obtain a total of 18 topologically distinct phase portraits. We show that inside the class of all quadratic systems with the topology of the coefficients, there exists a neighborhood of the family of quadratic systems with a weak focus of third order and which may have graphics but no polycycle in the sense of [15] and no limit cycle, such that any quadratic system in this neighborhood has at most four limit cycles.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Miao:2004:PMA, author = "Tianxuan Miao", title = "Predual of the Multiplier Algebra of {$A_p(G)$} and Amenability", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "344--355", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-016-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a locally compact group $G$ and $1 < p < \infty$, let $A$_p$ (G)$ be the Herz-Fig{\`a}-Talamanca algebra and let $PM$_p$ (G)$ be its dual Banach space. For a Banach $A$_p$ (G)$-module $X$ of $PM$_p$ (G)$, we prove that the multiplier space $mathcal{M} (A$_p$ (G), X$^*$)$ is the dual Banach space of $Q$_X$$, where $Q$_X$$ is the norm closure of the linear span $A$_p$ (G) X$ of $u f$ for $u \in A$_p$ (G)$ and $f \in X$ in the dual of $mathcal{M} (A$_p$ (G), X$^*$)$. If $p=2$ and $PF$_p$ (G) subseteq X$, then $A$_p$ (G)X$ is closed in $X$ if and only if $G$ is amenable. In particular, we prove that the multiplier algebra $MA$_p$ (G)$ of $A$_p$ (G)$ is the dual of $Q$, where $Q$ is the completion of $L$^1$ (G)$ in the ||.|| $$_M$$-norm. $Q$ is characterized by the following: $f \in Q$ if an only if there are $u$_i$ \in A$_p$ (G)$ and $f$_i$ \in PF$_p$ (G)$ $(i=1,2,...)$ with sum$_{i=1}^\infty$ || u$_i$ ||$_{A p}$ (G) ||f$_i$ ||$_{PF p}$ (G) < \infty such that $f= sum$_{i=1}^\infty$ u$_i$ f$_i$$ on $MA$_p$ (G)$. It is also proved that if $A$_p$ (G)$ is dense in $MA$_p$ (G)$ in the associated $w$^*$$-topology, then the multiplier norm and ||.|| $_{A p}$ (G) -norm are equivalent on $A$_p$ (G)$ if and only if $G$ is amenable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Murty:2004:NAG, author = "M. Ram Murty and Filip Saidak", title = "Non-{Abelian} Generalizations of the {Erd{\H{o}}s--Kac} Theorem", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "356--372", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-017-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $a$ be a natural number greater than 1. Let $f$_a$ (n)$ be the order of $a$ mod $n$. Denote by $\omega(n)$ the number of distinct prime factors of $n$. Assuming a weak form of the generalised Riemann hypothesis, we prove the following conjecture of Erd{\"o}s and Pomerance: The number of $n \leq x$ coprime to $a$ satisfying $\alpha \leq frac{\omega(f$_a$ (n)) - (log log n)$^2$ /2} / {(log log n)$^{3/2}$ / \sqrt{3}} \leq \beta$ is asymptotic to ( frac{1} / {\sqrt{2 pi} int$_{\alpha}^{\beta}$ e$^{-t 2}$ /2 dt) frac{x phi(a)} / {a}, as $x$ tends to infinity.??}", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Orton:2004:EPW, author = "Louisa Orton", title = "An Elementary Proof of a Weak Exceptional Zero Conjecture", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "373--405", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-018-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we extend Darmon's theory of ``integration on $mathcal{H}$_p$ x mathcal{H}$'' to cusp forms $f$ of higher even weight. This enables us to prove a {``weak exceptional zero conjecture''}: that when the $p$-adic $L$-function of $f$ has an exceptional zero at the central point, the $mathcal{L}$-invariant arising is independent of a twist by certain Dirichlet characters.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pal:2004:TSE, author = "Ambrus P{\'a}l", title = "Theta Series, {Eisenstein} Series and {Poincar{\'e}} Series over Function Fields", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "406--430", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-019-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we extend Darmon's theory of ``integration on $mathcal{H}$_p$ x mathcal{H}$'' to cusp forms $f$ of higher even weight. This enables us to prove a ``weak exceptional zero conjecture'': that when the $p$-adic $L$-function of $f$ has an exceptional zero at the central point, the $mathcal{L}$-invariant arising is independent of a twist by certain Dirichlet characters. We construct analogues of theta series, Eisenstein series and Poincar{\'e} series for function fields of one variable over finite fields, and prove their basic properties.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rosenblatt:2004:GAS, author = "Joseph Rosenblatt and Michael Taylor", title = "Group Actions and Singular Martingales {II}, The Recognition Problem", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "431--448", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-020-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We continue our investigation in [RST] of a martingale formed by picking a measurable set $A$ in a compact group $G$, taking random rotates of $A$, and considering measures of the resulting intersections, suitably normalized. Here we concentrate on the inverse problem of recognizing $A$ from a small amount of data from this martingale. This leads to problems in harmonic analysis on $G$, including an analysis of integrals of products of Gegenbauer polynomials.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Demeter:2004:BCA, author = "Ciprian Demeter", title = "The Best Constants Associated with Some Weak Maximal Inequalities in Ergodic Theory", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "449--471", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-021-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce a new device of measuring the degree of the failure of convergence in the ergodic theorem along subsequences of integers. Relations with other types of bad behavior in ergodic theory and applications to weighted averages are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fonf:2004:IDP, author = "Vladimir P. Fonf and Libor Vesel{\'y}", title = "Infinite-Dimensional Polyhedrality", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "472--494", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-022-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper deals with generalizations of the notion of a polytope to infinite dimensions. The most general definition is the following: a bounded closed convex subset of a Banach space is called a $polytope$ if each of its finite-dimensional affine sections is a (standard) polytope. We study the relationships between eight known definitions of infinite-dimensional polyhedrality. We provide a complete isometric classification of them, which gives solutions to several open problems. An almost complete isomorphic classification is given as well (only one implication remains open).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gomi:2004:CAF, author = "Yasushi Gomi and Iku Nakamura and Ken-ichi Shinoda", title = "Coinvariant Algebras of Finite Subgroups of {$\SL(3, C)$}", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "495--528", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-023-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For most of the finite subgroups of SL( $3,$ {\bf C}), we give explicit formulae for the Molien series of the coinvariant algebras, generalizing McKay's formulae [McKay99] for subgroups of SU( $2$). We also study the $G$-orbit Hilbert scheme Hilb $$^G$$ ( {\bf C} $$^3$$) for any finite subgroup $G$ of SO( $3$), which is known to be a minimal (crepant) resolution of the orbit space {\bf C} $$^3$ /G$. In this case the fiber over the origin of the Hilbert-Chow morphism from Hilb $$^G$$ ( {\bf C} $$^3$$) to {\bf C} $$^3$ /G$ consists of finitely many smooth rational curves, whose planar dual graph is identified with a certain subgraph of the representation graph of $G$. This is an SO( $3$) version of the McKay correspondence in the SU( $2$) case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Martinez-Finkelshtein:2004:AMD, author = "A. Mart{\'\i}nez-Finkelshtein and V. Maymeskul and E. A. Rakhmanov and E. B. Saff", title = "Asymptotics for Minimal Discrete {Riesz} Energy on Curves in {$\R^d$}", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "529--552", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-024-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider the $s$-energy $E$ ( {\bf Z} $$_n$ ;s$) = $sum$_{i \neq j}$ K$ (|| $z$_{i,n}$-z$_{j,n}$$ || $;s$) for point sets {\bf Z}$_n$ = {z$_{k,n}$ :k=0,...,n} on certain compact sets $\Gamma$ in {\bf R}$^d$ having finite one-dimensional Hausdorff measure, where $K$ ( $t;s$)= $t$^{-s}$$, if $s > 0$, -ln $t,$ if $s=0,$ is the Riesz kernel. Asymptotics for the minimum $s$-energy and the distribution of minimizing sequences of points is studied. In particular, we prove that, for $s geq 1$, the minimizing nodes for a rectifiable Jordan curve $\Gamma$ distribute asymptotically uniformly with respect to arclength as $n \to \infty$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mohammadalikhani:2004:CRS, author = "Ramin Mohammadalikhani", title = "Cohomology Ring of Symplectic Quotients by Circle Actions", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "553--565", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-025-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this article we are concerned with how to compute the cohomology ring of a symplectic quotient by a circle action using the information we have about the cohomology of the original manifold and some data at the fixed point set of the action. Our method is based on the Tolman-Weitsman theorem which gives a characterization of the kernel of the Kirwan map. First we compute a generating set for the kernel of the Kirwan map for the case of product of compact connected manifolds such that the cohomology ring of each of them is generated by a degree two class. We assume the fixed point set is isolated; however the circle action only needs to be {``formally Hamiltonian''}. By identifying the kernel, we obtain the cohomology ring of the symplectic quotient. Next we apply this result to some special cases and in particular to the case of products of two dimensional spheres. We show that the results of Kalkman and Hausmann-Knutson are special cases of our result.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ni:2004:GMH, author = "Yilong Ni", title = "Geodesics in a Manifold with {Heisenberg} Group as Boundary", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "566--589", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-026-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Heisenberg group is considered as the boundary of a manifold. A class of hypersurfaces in this manifold can be regarded as copies of the Heisenberg group. The properties of geodesics in the interior and on the hypersurfaces are worked out in detail. These properties are strongly related to those of the Heisenberg group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ni:2004:HKG, author = "Yilong Ni", title = "The Heat Kernel and {Green's} Function on a Manifold with {Heisenberg} Group as Boundary", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "590--611", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-027-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the Riemannian Laplace--Beltrami operator $L$ on a Riemannian manifold with Heisenberg group $H$_1$$ as boundary. We calculate the heat kernel and Green's function for $L$, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of $H$_1$$. We also restrict $L$ to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pal:2004:SPP, author = "Ambrus P{\'a}l", title = "Solvable Points on Projective Algebraic Curves", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "612--637", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-028-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus $g$, when $g$ is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic $p$ has a divisor of degree prime to $6p$ defined over a solvable extension.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sniatycki:2004:MRP, author = "J{\k{e}}drzej {\'S}niatycki", title = "Multisymplectic Reduction for Proper Actions", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "638--654", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-029-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider symmetries of the Dedonder equation arising from variational problems with partial derivatives. Assuming a proper action of the symmetry group, we identify a set of reduced equations on an open dense subset of the domain of definition of the fields under consideration. By continuity, the Dedonder equation is satisfied whenever the reduced equations are satisfied.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Tao:2004:NPS, author = "Xiangxing Tao and Henggeng Wang", title = "On the {Neumann} Problem for the {Schr{\"o}dinger} Equations with Singular Potentials in {Lipschitz} Domains", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "655--672", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-030-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider the Neumann problem for the Schr{\"o}dinger equations $-\Delta u+Vu=0$, with singular nonnegative potentials $V$ belonging to the reverse H{\"o}lder class {\bf B}$_n$, in a connected Lipschitz domain $\Omega subset$ {\bf R} $$^n$$. Given boundary data $g$ in $H^p$ or $L^p$ for $1 - epsilon < p \leq 2$, where $0 < epsilon < 1/n$, it is shown that there is a unique solution, $u$, that solves the Neumann problem for the given data and such that the nontangential maximal function of $nabla u$ is in $L^p$ ( $partial \Omega$). Moreover, the uniform estimates are found.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cali:2004:DSS, author = "{\'E}lie Cali", title = "{D}{\'e}faut de semi-stabilit{\'e} des courbes elliptiques dans le cas non ramifi{\'e}. ({French}) [{Semi-stability} failure of elliptic curves in the unbranched case]", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "673--698", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-031-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let ${\overline Q}$_2$$ be an algebraic closure of $Q$_2$$ and $K$ be an unramified finite extension of $Q$_2$$ included in ${\overline Q}$_2$$. Let $E$ be an elliptic curve defined over $K$ with additive reduction over $K$, and having an integral modular invariant. Let us denote by $K$_{nr}$$ the maximal unramified extension of $K$ contained in ${\overline Q}$_2$$. There exists a smallest finite extension $L$ of $K$_{nr}$$ over which $E$ has good reduction. We determine in this paper the degree of the extension $L/K$_{nr}$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Gaspari:2004:BFH, author = "Thierry Gaspari", title = "{Bump} Functions with {H{\"o}lder} Derivatives", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "699--715", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-032-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the range of the gradients of a $C$^{1, \alpha}$$-smooth bump function defined on a Banach space. We find that this set must satisfy two geometrical conditions: It can not be too flat and it satisfies a strong compactness condition with respect to an appropriate distance. These notions are defined precisely below. With these results we illustrate the differences with the case of $C$^1$$-smooth bump functions. Finally, we give a sufficient condition on a subset of $X$^*$$ so that it is the set of the gradients of a $C$^{1,1}$$-smooth bump function. In particular, if $X$ is an infinite dimensional Banach space with a $C$^{1,1}$$-smooth bump function, then any convex open bounded subset of $X$^*$$ containing 0 is the set of the gradients of a $C$^{1,1}$$-smooth bump function.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Guardo:2004:FPT, author = "Elena Guardo and Adam {Van Tuyl}", title = "Fat Points in {$\mathbb{P}^1 \times \mathbb{P}^1$} and Their {Hilbert} Functions", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "716--741", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-033-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the Hilbert functions of fat points in ${\mathbb p}$^1$ x {\mathbb p}$^1$$. If $Z subseteq {\mathbb p}$^1$ x {\mathbb p}$^1$$ is an arbitrary fat point scheme, then it can be shown that for every $i$ and $j$ the values of the Hilbert function $H$_Z$ (l,j)$ and $H$_Z$ (i,l)$ eventually become constant for $l > > 0$. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in ${\mathbb p}$^1$ x {\mathbb p}$^1$$. This enables us to compute all but a finite number values of $H$_Z$$ without using the coordinates of points. We also characterize the ACM fat point schemes sing our description of the eventual behaviour. In fact, in the case that $Z subseteq {\mathbb p}$^1$ x {\mathbb p}$^1$$ is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jiang:2004:SCC, author = "Chunlan Jiang", title = "Similarity Classification of {Cowen--Douglas} Operators", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "742--775", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-034-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $cal{H}$ be a complex separable Hilbert space and $cal{L} cal{H}$ denote the collection of bounded linear operators on $cal{H}$. An operator $A$ in $cal{L} cal{H}$ is said to be strongly irreducible, if $cal{A}$^\prime$ (T)$, the commutant of $A$, has no non-trivial idempotent. An operator $A$ in $cal{L} cal{H}$ is said to a Cowen-Douglas operator, if there exists \Omega, a connected open subset of $C$, and $n$, a positive integer, such that (a) $\Omega{subset}{\sigma}(A)= z \in C; A-z$ not invertible; (b) ran $(A-z)= cal{H},$ for $z$ in $\Omega$; (c) $bigvee$_{z \in \Omega}$ ker (A-z) = cal{H}$ and (d) $dim ker (A-z) = n$ for $z$ in $\Omega$. In the paper, we give a similarity classification of strongly irreducible Cowen-Douglas operators by using the $K$_0$$-group of the commutant algebra as an invariant.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lim:2004:BAR, author = "Yongdo Lim", title = "Best Approximation in {Riemannian} Geodesic Submanifolds of Positive Definite Matrices", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "776--793", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-035-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold $mathrm{Sym}(n,{Bbb R})$^{++}$$ of positive definite matrices. An explicit calculation for the minimal distance function from the geodesic submanifold $mathrm{Sym}(p,{\mathbb R})$^{++}$ x$ $mathrm{Sym}(q,{\mathbb R})$^{++}$$ block diagonally embedded in $mathrm{Sym}(n,{\mathbb R})$^{++}$$ is given in terms of metric and spectral geometric means, Cayley transform, and Schur complements of positive definite matrices when $p \leq 2$ or $q \leq 2$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Michel:2004:SCB, author = "Laurent Michel", title = "Semi-Classical Behavior of the Scattering Amplitude for Trapping Perturbations at Fixed Energy", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "794--824", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-036-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the semi-classical behavior as $h rightarrow 0$ of the scattering amplitude $f(\theta, \omega, \lambda, h)$ associated to a Schr{\"o}dinger operator $P(h) = - 1/2 h$^2$ \Delta + V(x)$ with short-range trapping perturbations. First we realize a spatial localization in the general case and we deduce a bound of the scattering amplitude on the real line. Under an additional assumption on the resonances, we show that if we modify the potential $V(x)$ in a domain lying behind the barrier ${x:V(x) > \lambda}$, the scattering amplitude $f(\theta, \omega, \lambda, h)$ changes by a term of order $O (h$^\infty$)$. Under an escape assumption on the classical trajectories incoming with fixed direction \omega, we obtain an asymptotic development of $f(\theta, \omega, \lambda, h)$ similar to the one established in thenon-trapping case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Penot:2004:DPO, author = "Jean-Paul Penot", title = "Differentiability Properties of Optimal Value Functions", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "825--842", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-037-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. Such a strengthening is required in order to obtain genericity results.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ruan:2004:TDR, author = "Zhong-Jin Ruan", title = "Type Decomposition and the Rectangular {AFD} Property for {{$W^*$}-TRO}'s", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "843--870", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-038-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the type decomposition and the rectangular AFD property for $W$^*$$-TRO's. Like von Neumann algebras, every $W$^*$$-TRO can be uniquely decomposed into the direct sum of $W$^*$$-TRO's of type $I$, type $II$, and type $III$. We may further consider $W$^*$$-TRO's of type $I$_{m, n}$$ with cardinal numbers $m$ and $n$, and consider $W$^*$$-TRO's of type $II$_{\lambda, \mu}$$ with $\lambda, \mu = 1$ or $\infty$. It is shown that every separable stable $W$^*$$-TRO (which includes type $I$_{\infty, \infty}$$, type $II$_{\infty, \infty}$$ and type $III$) is TRO-isomorphic to a von Neumann algebra. We also introduce the rectangular version of the approximately finite dimensional property for $W$^*$$-TRO's. One of our major results is to show that a separable $W$^*$$-TRO is injective if and only if it is rectangularly approximately finite dimensional. As a consequence of this result, we show that a dual operator space is injective if and only if its operator predual is a rigid rectangular $cal{OL}$_{1, 1$^+$}$$ space (equivalently, a rectangular $cal{OL}$_{1, 1$^+$}$$ space).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Schocker:2004:LEK, author = "Manfred Schocker", title = "{Lie} Elements and {Knuth} Relations", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "871--882", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-039-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A coplactic class in the symmetric group $Sym$_n$$ consists of all permutations in $Sym$_n$$ with a given Schensted $Q$-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of $Sym$_n$$ which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Reutenauer and the coplactic algebra introduced by Poirier and Reutenauer is the direct sum of all Solomon descent algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Tandra:2004:KTC, author = "Haryono Tandra and William Moran", title = "{Kirillov} Theory for a Class of Discrete Nilpotent Groups", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "883--896", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-040-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper is concerned with the Kirillov map for a class of torsion-free nilpotent groups $G$. $G$ is assumed to be discrete, countable and $pi$-radicable, with $pi$ containing the primes less than or equal to the nilpotence class of $G$. In addition, it is assumed that all of the characters of $G$ have idempotent absolute value. Such groups are shown to be plentiful.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Borwein:2004:FEA, author = "Jonathan M. Borwein and David Borwein and William F. Galway", title = "Finding and Excluding $b$-ary {Machin}-Type Individual Digit Formulae", journal = j-CAN-J-MATH, volume = "56", number = "5", pages = "897--925", month = oct, year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-041-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Constants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe ({\em BBP formulae\/} to a given base $b$) have interesting computational properties, such as allowing single digits in their base $b$ expansion to be independently computed, and there are hints that they should be {\em normal\/} numbers, {\em i.e.}, that their base $b$ digits are randomly distributed. We study a formally limited subset of BBP formulae, which we call {\em Machin-type BBP formulae}, for which it is relatively easy to determine whether or not a given constant $\kappa$ has a Machin-type BBP formula. In particular, given $b \in \mathbb{N}$, $b > 2$, $b$ not a proper power, a $b$-ary Machin-type BBP arctangent formula for $\kappa$ is a formula of the form $\kappa = \sum_m a_m \arctan(-b^{-m})$, $a_m \in \mathbb{Q}$, while when $b = 2$, we also allow terms of the form $a_m \arctan(1 / (1 - 2^m))$. Of particular interest, we show that $\pi$ has no Machin-type BBP arctangent formula when $b \neq 2$. To the best of our knowledge, when there is no Machin-type BBP formula for a constant then no BBP formula of any form is known for that constant.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", remark = "This paper established the result that there are no degree-1 BBP-type formulas for $\pi$, except when the base is 2 (or an integer power thereof).", } @Article{Hadfield:2004:HRA, author = "Tom Hadfield", title = "{$K$}-Homology of the Rotation Algebras {{$A_{\theta}$}}", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "926--944", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-042-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the $K$-homology of the rotation algebras $A_\theta$ using the six-term cyclic sequence for the $K$-homology of a crossed product by ${\bf Z}$. In the case that $\theta$ is irrational, we use Pimsner and Voiculescu's work on AF-embeddings of the $A_\theta$ to search for the missing generator of the even $K$-homology.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Helminck:2004:SQA, author = "Aloysius G. Helminck and Gerald W. Schwarz", title = "Smoothness of Quotients Associated with a Pair of Commuting Involutions", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "945--962", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-043-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\sigma$, $\theta$ be commuting involutions of the connected semisimple algebraic group $G$ where $\sigma$, $\theta$ and $G$ are defined over an algebraically closed field ${underbar k}$, Char ${underbar k} = 0$. Let $H := G^\sigma$ and $K := G^\theta$ be the fixed point groups. We have an action $(H x K) x G \to G$, where $((h,k),g) \mapsto hgk \inv$, $h \in H$, $k \in K$, $g \in G$. Let $quot G{(H x K)}$ denote the categorical quotient Spec $cal{O}(G)$^{H x K}$$. We determine when this quotient is smooth. Our results are a generalization of those of Steinberg [Ste75], Pittie [Pit72] and Richardson [Ric82] in the symmetric case where $\sigma = \theta$ and $H = K$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ishiwata:2004:BET, author = "Satoshi Ishiwata", title = "A {Berry--Esseen} Type Theorem on Nilpotent Covering Graphs", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "963--982", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-044-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove an estimate for the speed of convergence of the transition probability for a symmetric random walk on a nilpotent covering graph. To obtain this estimate, we give a complete proof of the Gaussian bound for the gradient of the Markov kernel.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Junge:2004:FTU, author = "Marius Junge", title = "{Fubini}'s Theorem for Ultraproducts of Noncommutative {$L_p$}-Spaces", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "983--1021", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-045-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $({\cal M}$_i$)$_{i \in I}$$, $({\cal N}$_j$)$_{j \in J}$$ be families of von Neumann algebras and ${\cal U}$, ${\cal U}'$ be ultrafilters in $I$, $J$, respectively. Let $1 \leq p < \infty$ and $n \in N$. Let $x$_1$,...,x$_n$$ in $prod L$_p$ ({\cal M}$_i$)$ and $y$_1$,...,y$_n$$ in $prod L$_p$ ({\cal N}$_j$)$ be bounded families. We show the following equality lim$_{i,{\cal U}}$ lim$_{j, {\cal U}'}$ | sum$_{k = 1}^n$ x$_k$ (i) \otimes y$_k$ (j) |$_{L p}$ ({\cal M}$_i$ \otimes {\cal N}$_j$) = lim$_{j, {\cal U}'}$ lim$_{i, {\cal U}}$ | sum$_{k = 1}^n$ x$_k$ (i) \otimes y$_k$ (j) |$_{L p}$ ({\cal M}$_i$ \otimes {\cal N}$_j$). For $p = 1$ this Fubini type result is related to the local reflexivity of duals of $C$^*$$-algebras. This fails for $p = \infty$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Matignon:2004:NOS, author = "D. Matignon and N. Sayari", title = "Non-Orientable Surfaces and {Dehn} Surgeries", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1022--1033", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-046-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a knot in $S$^3$$. This paper is devoted to Dehn surgeries which create 3-manifolds containing a closed non-orientable surface $hat S$. We look at the slope $p/q$ of the surgery, the Euler characteristic $\chi(hat S)$ of the surface and the intersection number $s$ between $hat S$ and the core of the Dehn surgery. We prove that if $\chi(hat S) \geq 15 - 3q$, then $s = 1$. Furthermore, if $s = 1$ then $q \leq 4 - 3 \chi(hat S)$ or $K$ is cabled and $q \leq 8 - 5 \chi(hat S)$. As consequence, if $K$ is hyperbolic and $\chi(hat S) = -1$, then $q \leq 7$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rouleux:2004:SCI, author = "Michel Rouleux", title = "Semi-classical Integrability,Hyperbolic Flows and the {Birkhoff} Normal Form", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1034--1067", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-047-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that a Hamiltonian p \in C$^\infty$ (T$^*$ {\bf R}$^n$) is locally integrable near a non-degenerate critical point $rho$_0$$ of the energy, provided that the fundamental matrix at $rho$_0$$ has rationally independent eigenvalues, none purely imaginary. This is done by using Birkhoff normal forms, which turn out to be convergent in the $C$^\infty$$ sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transformation. Then we investigate the complex case, showing that when $p$ is holomorphic near rho$_0$ \in T$^*$ {\bf C}$^n$, then $Re p$ becomes integrable in the complex domain for real times, while the Birkhoff series and the Birkhoff transforms may not converge, $i.e.,$ $p$ may not be integrable. These normal forms also hold in the semi-classical frame.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Steinbach:2004:REG, author = "Anja Steinbach and Hendrik {Van Maldeghem}", title = "Regular Embeddings of Generalized Hexagons", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1068--1093", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-048-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type G $$_2$$, $$^3$$ D $$_4$$ and $$^6$$ D $$_4$$ (and occurring in projective dimensions $5,6,7$), we find new examples in unbounded dimension related to the mixed groups of type G $$_2$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Thomas:2004:CLI, author = "Hugh Thomas", title = "Cycle-Level Intersection Theory for Toric Varieties", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1094--1120", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-049-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor with an invariant cycle on a toric variety. For a toric variety defined by a fan in $N$, the choice consists of giving an inner product or a complete flag for $M$_{{\mathbb Q}}$ = {\mathbb Q} t Hom(N,{\mathbb Z})$, or more generally giving for each cone $\sigma$ in the fan a linear subspace of $M$_{\sigma}$$ complementary to $\sigma$^{perp}$$, satisfying certain compatibility conditions. We show that these intersection cycles have properties analogous to the usual intersections modulo rational equivalence. If $X$ is simplicial (for instance, if $X$ is non-singular), we obtain a commutative ring structure to the invariant cycles of $X$ with rational coefficients. This ring structure determines cycles representing certain characteristic classes of the toric variety. We also discuss how to define intersection cycles that require no choices, at the expense of increasing the size of the coefficient field.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chaumat:2004:DPP, author = "Jacques Chaumat and Anne-Marie Chollet", title = "Division par un polyn{\^o}me hyperbolique. ({French}) [{Division} by a hyperbolic polynomial]", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1121--1144", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-050-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "On se donne un intervalle ouvert non vide $\omega$ de $\mathbb R$, un ouvert connexe non vide $\Omega$ de $\mathbb R$_s$$ et un polyn{\^o}me unitaire $P$_m$ (z, lambda) = z$^m$ + a$_1$ (lambda)z$^{m-1}$ = +\dots + a$_{m-1}$ (lambda) z + a$_m$ (lambda),$ de degr{\'e} $m > 0$, d{\'e}pendant du param{\`e}tre $lambda \in \Omega$. Un tel polyn{\^o}me est dit $\omega$-hyperbolique si, pour tout $lambda \in \Omega$, ses racines sont r{\'e}elles et appartiennent {\`a} $\omega$. On suppose que les fonctions $a$_k$$, $k = 1, \dots, m$, appartiennent {\`a} une classe ultradiff{\'e}rentiable $C$_M$ (\Omega)$. On s`int{\'e}resse au probl{\`e}me suivant. Soit $f$ appartient {\`a} $C$_M$ (\Omega)$, existe-t-il des fonctions $Q$_f$$ et $R$_{f,k}$$, $k = 0, \dots, m - 1$, appartenant respectivement {\`a} $C$_M$ (\omega \times \Omega)$ et {\`a} $C$_M$ (\Omega)$, telles que l'on ait, pour $(x, lambda) \in \omega \times \Omega$, $f(x) = P$_m$ (x,lambda) Q$_f$ (x,lambda) + \sum$^{m-1}_{k = 0}$ x$^k$ R$_{f,k}$ (lambda)?$ On donne ici une r{\'e}ponse positive d{\`e}s que le polyn{\^o}me est $\omega$-hyperbolique, que la class untradiff{\'e}ren\-tiable soit quasi-analytique ou non; on obtient alors, des exemples d'id{\'e}aux ferm{\'e}s dans $C$_M$ (\mathbb R$^n$)$. On compl{\`e}te ce travail par une g{\'e}n{\'e}ralisation d'un r{\'e}sultat de C. L. Childress dans le cadre quasi-analytique et quelques remarques.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Daigle:2004:LHP, author = "Daniel Daigle and Peter Russell", title = "On Log {$\mathbb Q$}-Homology Planes and Weighted Projective Planes", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1145--1189", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-051-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We classify normal affine surfaces with trivial Makar-Limanov invariant and finite Picard group of the smooth locus, realizing them as open subsets of weighted projective planes. We also show that such a surface admits, up to conjugacy, one or two $G$_a$$-actions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Frank:2004:MFS, author = "G{\"u}nter Frank and Xinhou Hua and R{\'e}mi Vaillancourt", title = "Meromorphic Functions Sharing the Same Zeros and Poles", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1190--1227", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-052-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, Hinkkanen's problem (1984) is completely solved, $i.e.,$ it is shown that any meromorphic function $f$ is determined by its zeros and poles and the zeros of f$^{(j)}$ for $j = 1,2,3,4$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ho:2004:CMS, author = "Nan-Kuo Ho and Chiu-Chu Melissa Liu", title = "On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1228--1236", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-053-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the connectedness of the moduli space of gauge equivalence classes of flat $G$-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kishimoto:2004:CSA, author = "Akitaka Kishimoto", title = "Central Sequence Algebras of a Purely Infinite Simple {$C^*$}-algebra", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1237--1258", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-054-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We are concerned with a unital separable nuclear purely infinite simple $C$^*$$-algebra\ $A$ satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two $central$ projections in $A$ are equivalent by a $central$ partial isometry. Our second result shows that the K-theory of the central sequence algebra $A$^'$ \cap A$^{\omega}$$ (for an $\omega \in \beta \N \setminus \N$ and its $fixed point$ algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in [12].", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Paterson:2004:FAL, author = "Alan L. T. Paterson", title = "The {Fourier} Algebra for Locally Compact Groupoids", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1259--1289", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-055-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce and investigate using Hilbert modules the properties of the $Fourier algebra$ $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Scull:2004:EFA, author = "Laura Scull", title = "Equivariant Formality for Actions of Torus Groups", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1290--1307", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-056-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper contains a comparison of several definitions of equivariant formality for actions of torus groups. We develop and prove some relations between the definitions. Focusing on the case of the circle group, we use $S$^1$$-equivariant minimal models to give a number of examples of $S$^1$$-spaces illustrating the properties of the various definitions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhao:2004:VMH, author = "Jianqiang Zhao", title = "Variations of Mixed {Hodge} Structures of Multiple Polylogarithms", journal = j-CAN-J-MATH, volume = "56", number = "??", pages = "1308--1338", month = "????", year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-057-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall $explicitly$ determine these structures related to multiple logarithms and some other multiple polylogarithms of lower weights. The purpose of this explicit construction is to give some important applications: First we study the limit of mixed Hodge-Tate structures and make a conjecture relating the variations of mixed Hodge-Tate structures of multiple logarithms to those of general multiple $poly$ logarithms. Then following Deligne and Beilinson we describe an approach to defining the single-valued real analytic version of the multiple polylogarithms which generalizes the well-known result of Zagier on classical polylogarithms. In the process we find some interesting identities relating single-valued multiple polylogarithms of the same weight $k$ when $k = 2$ and 3. At the end of this paper, motivated by Zagier's conjecture we pose a problem which relates the special values of multiple Dedekind zeta functions of a number field to the single-valued version of multiple polylogarithms.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2004:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2004 --- pour 2004", journal = j-CAN-J-MATH, volume = "56", number = "6", pages = "1339--1342", month = dec, year = "2004", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2004-058-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:11 MDT 2011", bibsource = "http://cms.math.ca/cjm/v56/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Alberich-Carraminana:2005:EDA, author = "Maria Alberich-Carrami{\~n}ana and Joaquim Ro{\'e}", title = "Enriques Diagrams and Adjacency of Planar Curve Singularities", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "3--16", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-001-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study adjacency of equisingularity types of planar complex curve singularities in terms of their Enriques diagrams. The goal is, given two equisingularity types, to determine whether one of them is adjacent to the other. For linear adjacency a complete answer is obtained, whereas for arbitrary (analytic) adjacency a necessary condition and a sufficient condition are proved. We also obtain new examples of exceptional deformations, $i.e.,$ singular curves of type $mathcal{D}'$ that can be deformed to a curve of type $mathcal{D}$ without $mathcal{D}'$ being adjacent to $mathcal{D}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bedos:2005:ACA, author = "Erik B{\'e}dos and Roberto Conti and Lars Tuset", title = "On Amenability and Co-Amenability of Algebraic Quantum Groups and Their Corepresentations", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "17--60", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-002-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce and study several notions of amenability for unitary corepresentations and $*$-representations of algebraic quantum groups, which may be used to characterize amenability and co-amenability for such quantum groups. As a background for this study, we investigate the associated tensor $C$^*$$-categories.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Binding:2005:OSS, author = "Paul Binding and Vladimir Strauss", title = "On Operators with Spectral Square but without Resolvent Points", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "61--81", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-003-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Decompositions of spectral type are obtained for closed Hilbert space operators with empty resolvent set, but whose square has closure which is spectral. Krein space situations are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fallat:2005:JST, author = "Shaun M. Fallat and Michael I. Gekhtman", title = "{Jordan} Structures of Totally Nonnegative Matrices", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "82--98", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-004-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "An $n x n$ matrix is said to be totally nonnegative if every minor of $A$ is nonnegative. In this paper we completely characterize all possible Jordan canonical forms of irreducible totally nonnegative matrices. Our approach is mostly combinatorial and is based on the study of weighted planar diagrams associated with totally nonnegative matrices.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fegan:2005:SOO, author = "H. D. Fegan and B. Steer", title = "Second Order Operators on a Compact {Lie} Group", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "99--113", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-005-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We describe the structure of the space of second order elliptic differential operators on a homogenous bundle over a compact Lie group. Subject to a technical condition, these operators are homotopic to the Laplacian. The technical condition is further investigated, with examples given where it holds and others where it does not. Since many spectral invariants are also homotopy invariants, these results provide information about the invariants of these operators.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Flaschka:2005:BFS, author = "Hermann Flaschka and John Millson", title = "Bending Flows for Sums of Rank One Matrices", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "114--158", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-006-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study certain symplectic quotients of $n$-fold products of complex projective $m$-space by the unitary group acting diagonally. After studying nonemptiness and smoothness of these quotients we construct the action-angle variables, defined on an open dense subset, of an integrable Hamiltonian system. The semiclassical quantization of this system reporduces formulas from the representation theory of the unitary group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jantzen:2005:DSI, author = "Chris Jantzen", title = "Duality and Supports of Induced Representations for Orthogonal Groups", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "159--179", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-007-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we construct a duality for $p$-adic orthogonal groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Somodi:2005:SWS, author = "Marius Somodi", title = "On the Size of the Wild Set", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "180--203", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-008-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the $minimum number of wild primes$. Earlier investigations have established lower bounds for this number. In this paper an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered to be an exact formula for the minimum number of wild primes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Xiong:2005:DBC, author = "Jie Xiong and Xiaowen Zhou", title = "On the Duality between Coalescing {Brownian} Motions", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "204--224", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-009-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Booss-Bavnbek:2005:UFO, author = "Bernhelm Booss-Bavnbek and Matthias Lesch and John Phillips", title = "Unbounded {Fredholm} Operators and Spectral Flow", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "225--250", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-010-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the gap (= {``projection norm''} = {``graph distance''}) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show the surprising result that this space is connected in contrast to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cocos:2005:SNR, author = "M. Cocos", title = "Some New Results on {$L^2$} Cohomology of Negatively Curved {Riemannian} Manifolds", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "251--266", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-011-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The present paper is concerned with the study of the $L$^2$$ cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial $L$^2$$ cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Conrad:2005:PEP, author = "Keith Conrad", title = "Partial {Euler} Products on the Critical Line", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "267--297", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-012-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve $L$-function at $s = 1$. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the $L$-function and that the constant in the asymptotics has an unexpected factor of $\sqrt{2}$. We extend Goldfeld's theorem to an analysis of partial Euler products for a typical $L$-function along its critical line. The general $\sqrt{2}$ phenomenon is related to second moments, while the asymptotic behavior (over number fields) is proved to be equivalent to a condition that in a precise sense seems much deeper than the Riemann hypothesis. Over function fields, the Euler product asymptotics can sometimes be proved unconditionally.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kumchev:2005:WGP, author = "Angel V. Kumchev", title = "On the {Waring--Goldbach} Problem: Exceptional Sets for Sums of Cubes and Higher Powers", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "298--327", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-013-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate exceptional sets in the Waring--Goldbach problem. For example, in the cubic case, we show that all but $O(N$^{79/84 + epsilon}$)$ integers subject to the necessary local conditions can be represented as the sum of five cubes of primes. Furthermore, we develop a new device that leads easily to similar estimates for exceptional sets for sums of fourth and higher powers of primes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kuo:2005:CBS, author = "Wentang Kuo and M. Ram Murty", title = "On a Conjecture of {Birch} and {Swinnerton-Dyer}", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "328--337", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-014-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $E /(\mathbb Q)$ be an elliptic curve defined by the equation $y$^2$ = x$^3$ + ax + b$. For a prime $p, p \nmid \Delta = -16(4a$^3$ + 27b$^2$) \neq 0$, define $N$_p$ = p + 1 -a$_p$ = |E((\mathbb F)$_p$)|.$ As a precursor to their celebrated conjecture, Birch and Swinnerton-Dyer originally conjectured that for some constant $c$, $\prod$_{p \leq x, p \nmid \Delta}$ (N$_p$)/p \sim c (log x)$^r$, \quad x \to \infty.$ Let $\alpha$_p$$ and $\beta$_p$$ be the eigenvalues of the Frobenius at $p$. Define $tilde{c}$_n$ =$ { ${\alpha$_p^k$ + \beta$_p^k$}/k n =p$^k$,$ $p$ is a prime, $k$ is a natural number, $p \nmid \Delta$. $0$ otherwise.} and $tilde{C}(x) = sum$_{n \leq x}$ tilde{c}$_n$$. In this paper, we establish the equivalence between the conjecture and the condition $tilde{C}(x) = mathbf{o}(x)$. The asymptotic condition is indeed much deeper than what we know so far or what we can know under the analogue of the Riemann hypothesis. In addition, we provide an oscillation theorem and an $\Omega$ theorem which relate to the constant $c$ in the conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lange:2005:CES, author = "Tanja Lange and Igor E. Shparlinski", title = "Certain Exponential Sums and Random Walks on Elliptic Curves", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "338--350", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-015-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a given elliptic curve $E$, we obtain an upper bound on the discrepancy of sets of multiples $z$_s$ G$ where $z$_s$$ runs through a sequence $Z = (z$_1$, ..., z$_T$)$ such that $k z$_1$, ..., kz$_T$$ is a permutation of $z$_1$, ..., z$_T$$, both sequences taken modulo $t$, for sufficiently many distinct values of $k$ modulo $t$. We apply this result to studying an analogue of the power generator over an elliptic curve. These results are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lin:2005:ESA, author = "Huaxin Lin", title = "Extensions by Simple {$C^*$}-Algebras: Quasidiagonal Extensions", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "351--399", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-016-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $A$ be an amenable separable $C$^*$$-algebra and $B$ be a non-unital but $\sigma$-unital simple $C$^*$$-algebra with continuous scale. We show that two essential extensions $tau$_1$$ and $tau$_2$$ of $A$ by $B$ are approximately unitarily equivalent if and only if $[tau$_1$ ]=[tau$_2$ ]$ in $KL(A, M(B)/B).$ If $A$ is assumed to satisfy the Universal Coefficient Theorem, there is a bijection from approximate unitary equivalence classes of the above mentioned extensions to $KL(A, M(B)/B)$. Using $KL(A, M(B)/B)$, we compute exactly when an essential extension is quasidiagonal. We show that quasidiagonal extensions may not be approximately trivial. We also study the approximately trivial extensions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sabourin:2005:GC, author = "Sindi Sabourin", title = "Generalized $k$-Configurations", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "400--415", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-017-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we find configurations of points in $n$-dimensional projective space ( ${\mathbb P}$^n$$) which simultaneously generalize both $k$-configurations and reduced $0$-dimensional complete intersections. Recall that $k$-configurations in ${\mathbb P}$^2$$ are disjoint unions of distinct points on lines and in ${\mathbb P}$^n$$ are inductively disjoint unions of $k$-configurations on hyperplanes, subject to certain conditions. Furthermore, the Hilbert function of a $k$-configuration is determined from those of the smaller $k$-configurations. We call our generalized constructions $k$_D$$-configurations, where $D = {d$_1$, ...,d$_r$}$ (a set of $r$ positive integers with repetition allowed) is the type of a given complete intersection in ${\mathbb P}$^n$$. We show that the Hilbert function of any $k$_D$$-configuration can be obtained from those of smaller $k$_D$$-configurations. We then provide applications of this result in two different directions, both of which are motivated by corresponding results about $k$-configurations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wise:2005:AFP, author = "Daniel T. Wise", title = "Approximating Flats by Periodic Flats in ${\CAT}(0)$ Square Complexes", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "416--448", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-018-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate the problem of whether every immersed flat plane in a nonpositively curved square complex is the limit of periodic flat planes. Using a branched cover, we reduce the problem to the case of $VH$-complexes. We solve the problem for malnormal and cyclonormal $VH$-complexes. We also solve the problem for complete square complexes using a different approach. We give an application towards deciding whether the elements of fundamental groups of the spaces we study have commuting powers. We note a connection between the flat approximation problem and subgroup separability.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Alkan:2005:SGF, author = "Emre Alkan", title = "On the Sizes of Gaps in the {Fourier} Expansion of Modular Forms", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "449--470", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-019-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $f = sum$_{n = 1}^\infty$ a$_f$ (n)q$^n$$ be a cusp form with integer weight $k \geq 2$ that is not a linear combination of forms with complex multiplication. For $n \geq 1$, let $i$_f$ (n)= {i : a$_f$ (n+j) = 0$ for all $0 \leq j \leq i}$ if $a$_f$ (n) = 0,$ $0$ otherwise. Concerning bounded values of $i$_f$ (n)$ we prove that for $epsilon > 0$ there exists $M = M(epsilon,f)$ such that $# {n \leq x : i$_f$ (n) \leq M} \geq (1 - epsilon) x$. Using results of Wu, we show that if $f$ is a weight 2 cusp form for an elliptic curve without complex multiplication, then $i$_f$ (n) ll$_{f, epsilon}$ n$^{51/134 + epsilon}$$. Using a result of David and Pappalardi, we improve the exponent to $1/3$ for almost all newforms associated to elliptic curves without complex multiplication. Inspired by a classical paper of Selberg, we also investigate $i$_f$ (n)$ on the average using well known bounds on the Riemann Zeta function.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ciesielski:2005:SCS, author = "Krzysztof Ciesielski and Janusz Pawlikowski", title = "Small Coverings with Smooth Functions under the Covering Property Axiom", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "471--493", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-020-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In the paper we formulate a Covering Property Axiom, CPA$_{prism}$, which holds in the iterated perfect set model, and show that it implies the following facts, of which (a) and (b) are the generalizations of results of J. Steprans. (a) There exists a family $\cal F$ of less than continuum many $\cal C$^1$$ functions from $R$ to $R$ such that $R$^2$$ is covered by functions from $cal F$, in the sense that for every $(x,y) \in R$^2$$ there exists an $f \in {\cal F}$ such that either $f(x) = y$ or $f(y) = x$. (b) For every Borel function $f: R \to R$ there exists a family $\cal F$ of less than continuum many ``${\cal C}$^1$$'' functions ($i.e.,$ differentiable functions with continuous derivatives, where derivative can be infinite) whose graphs cover the graph of $f$. (c) For every $n > 0$ and a $D$^n$$ function $f: R \to R$ there exists a family $\cal F$ of less than continuum many ${\cal C}$^n$$ functions whose graphs cover the graph of $f$. We also provide the examples showing that in the above properties the smoothness conditions are the best possible. Parts (b), (c), and the examples are closely related to work of A. Olevskii.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Friedlander:2005:SFC, author = "John B. Friedlander and Henryk Iwaniec", title = "Summation Formulae for Coefficients of {$L$}-functions", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "494--505", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-021-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "With applications in mind we establish a summation formula for the coefficients of a general Dirichlet series satisfying a suitable functional equation. Among a number of consequences we derive a generalization of an elegant divisor sum bound due to F. V. Atkinson.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gross:2005:RHS, author = "Leonard Gross and Martin Grothaus", title = "Reverse Hypercontractivity for Subharmonic Functions", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "506--534", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-022-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Contractivity and hypercontractivity properties of semigroups are now well understood when the generator, $A$, is a Dirichlet form operator. It has been shown that in some holomorphic function spaces the semigroup operators, $e$^{-tA}$,$ can be bounded $below$ from $L^p$ to $L$^q$$ when $p,q$ and $t$ are suitably related. We will show that such lower boundedness occurs also in spaces of subharmonic functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kim:2005:LFN, author = "Henry H. Kim", title = "On Local {$L$}-Functions and Normalized Intertwining Operators", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "535--597", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-023-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we make explicit all $L$-functions in the Langlands--Shahidi method which appear as normalizing factors of global intertwining operators in the constant term of the Eisenstein series. We prove, in many cases, the conjecture of Shahidi regarding the holomorphy of the local $L$-functions. We also prove that the normalized local intertwining operators are holomorphic and non-vaninishing for $Re(s) \geq 1/2$ in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrum and determining poles of automorphic $L$-functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kornelson:2005:LSL, author = "Keri A. Kornelson", title = "Local Solvability of {Laplacian} Difference Operators Arising from the Discrete {Heisenberg} Group", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "598--615", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-024-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Differential operators $D$_x$$, $D$_y$$, and $D$_z$$ are formed using the action of the 3-dimensional discrete Heisenberg group $G$ on a set $S$, and the operators will act on functions on $S$. The Laplacian operator $L = D$_x^2$ + D$_y^2$ + D$_z^2$$ is a difference operator with variable differences which can be associated to a unitary representation of $G$ on the Hilbert space $L$^2$ (S)$. Using techniques from harmonic analysis and representation theory, we show that the Laplacian operator is locally solvable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Muic:2005:RGP, author = "Goran Mui{\'c}", title = "Reducibility of Generalized Principal Series", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "616--647", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-025-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we describe reducibility of non-unitary generalized principal series for classical $p$-adic groups in terms of the classification of discrete series due to Moeglin and Tadic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nevins:2005:BRP, author = "Monica Nevins", title = "Branching Rules for Principal Series Representations of {$SL(2)$} over a $p$-adic Field", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "648--672", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-026-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of $SL(2,k)$, for $k$ a $p$-adic field, to each of its two maximal compact subgroups (up to conjugacy). We identify these irreducible subrepresentations in the Kirillov-type classification of Shalika. We go on to explicitly describe the decomposition of the reducible principal series of $SL(2,k)$ in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Androulakis:2005:SSM, author = "G. Androulakis and E. Odell and Th. Schlumprecht and N. Tomczak-Jaegermann", title = "On the Structure of the Spreading Models of a {Banach} Space", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "673--707", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-027-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$. In particular we give an example of a reflexive $X$ so that all spreading models of $X$ contain $ell$_1$$ but none of them is isomorphic to $ell$_1$$. We also prove that for any countable set $C$ of spreading models generated by weakly null sequences there is a spreading model generated by a weakly null sequence which dominates each element of $C$. In certain cases this ensures that $X$ admits, for each ${\alpha} < {\omega}$_1$$, a spreading model $( {\SGMLtilde} x$_i^{({\alpha})}$)$_i$$ such that if ${\alpha} < {\beta}$ then $( {\SGMLtilde} x$_i^{({\alpha})}$)$_i$$ is dominated by (and not equivalent to) $( {\SGMLtilde} x$_i^{({\beta})}$)$_i$$. Some applications of these ideas are used to give sufficient conditions on a Banach space for the existence of a subspace and an operator defined on the subspace, which is not a compact perturbation of a multiple of the inclusion map.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Finster:2005:CEA, author = "Felix Finster and Margarita Kraus", title = "Curvature Estimates in Asymptotically Flat {Lorentzian} Manifolds", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "708--723", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-028-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider an asymptotically flat Lorentzian manifold of dimension $(1,3)$. An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Purnaprajna:2005:SRS, author = "B. P. Purnaprajna", title = "Some Results on Surfaces of General Type", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "724--749", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-029-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this article we prove some new results on projective normality, normal presentation and higher syzygies for surfaces of general type, not necessarily smooth, embedded by adjoint linear series. Some of the corollaries of more general results include: results on property $N$_p$$ associated to $K$_S$ \otimes B$^{otimes n}$$ where $B$ is base-point free and ample divisor with $B \otimes K$^*$$ $nef$, results for pluricanonical linear systems and results giving effective bounds for adjoint linear series associated to ample bundles. Examples in the last section show that the results are optimal.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sabourin:2005:STO, author = "Herv{\'e} Sabourin", title = "Sur la structure transverse {\`a} une orbite nilpotente adjointe. ({French}) [{On} the transverse structure of a nilpotent adjoint orbit]", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "750--770", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-030-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We are interested in Poisson structures to transverse nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature. Furthermore, in the case of $sl$_n$$, we construct some families of nilpotent orbits with quadratic transverse structures.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Schrohe:2005:RCE, author = "E. Schrohe and J. Seiler", title = "The Resolvent of Closed Extensions of Cone Differential Operators", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "771--811", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-031-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study closed extensions $underline A$ of an elliptic differential operator $A$ on a manifold with conical singularities, acting as an unbounded operator on a weighted $L$_p$$-space. Under suitable conditions we show that the resolvent $(lambda-underline A)$^{-1}$$ exists in a sector of the complex plane and decays like $1/|lambda|$ as $|lambda| \to \infty$. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of $underline A$. As an application we treat the Laplace--Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem $\dot{u} - \Delta u = f$, $u(0) = 0$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Trifkovic:2005:VIE, author = "Mak Trifkovi{\'c}", title = "On the Vanishing of $\mu$-Invariants of Elliptic Curves over {$\mathbb{Q}$}", journal = j-CAN-J-MATH, volume = "57", number = "4", pages = "812--843", month = aug, year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-032-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $E$_{/ {\mathbb Q}}$$ be an elliptic curve with good ordinary reduction at a prime $p > 2$. It has a well-defined Iwasawa $mu$-invariant $mu(E)$_p$$ which encodes part of the information about the growth of the Selmer group $Sel E{K$_n$}$ as $K$_n$$ ranges over the subfields of the cyclotomic ${\mathbb Z}p$-extension $K$_{\infty/{\mathbb Q}}$$. Ralph Greenberg has conjectured that any such $E$ is isogenous to a curve $E$^'$$ with $mu(E$^'$)$_p$ = 0$. In this paper we prove Greenberg's conjecture for infinitely many curves $E$ with a rational $p$-torsion point, $p = 3$ or 5, no two of our examples having isomorphic $p$-torsion. The core of our strategy is a partial explicit evaluation of the global duality pairing for finite flat group schemes over rings of integers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Williams:2005:PS, author = "Gordon Williams", title = "{Petrie} Schemes", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "844--870", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-033-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Petrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Gr{\"u}nbaum--Dress polyhedra, possess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhang:2005:HYM, author = "Xi Zhang", title = "{Hermitian} {Yang--Mills--Higgs} Metrics on Complete {K{\"a}hler} Manifolds", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "871--896", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-034-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact K{\"a}hler manifolds.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Berezhnoi:2005:RBI, author = "Evgenii I. Berezhnoi and Lech Maligranda", title = "Representation of {Banach} Ideal Spaces and Factorization of Operators", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "897--940", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-035-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calder{\'o}n--Lozanovskii construction. Factorization theorems for operators in spaces more general than the Lebesgue $L^p$ spaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt $A$_p$$ weights to reflexive Orlicz spaces. However, it turns out that for the scales far from $L^p$-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calder{\'o}n--Lozanovskii construction are involved in the proofs.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Berg:2005:STH, author = "Christian Berg and Antonio J. Dur{\'a}n", title = "Some Transformations of {Hausdorff} Moment Sequences and Harmonic Numbers", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "941--960", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-036-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: $T((a$_n$)$_n$) = 1/(a$_0$ + ... +a$_n$)$. We give some examples of Hausdorff moment sequences arising from the transformations and provide the corresponding measures: one of these sequences is the reciprocal of the harmonic numbers $(1+1/2 + ... + 1/(n+1))$^{-1}$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Borwein:2005:CMF, author = "Jonathan M. Borwein and Xianfu Wang", title = "Cone-Monotone Functions: Differentiability and Continuity", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "961--982", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-037-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone $K$ with non-empty interior. We also show that the set of nowhere $K$-monotone functions has a ${\sigma}$-porous complement in the space of continuous functions endowed with the uniform metric.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{anHuef:2005:SIT, author = "Astrid an Huef and Iain Raeburn and Dana P. Williams", title = "A Symmetric Imprimitivity Theorem for Commuting Proper Actions", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "983--1011", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-038-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove a symmetric imprimitivity theorem for commuting proper actions of locally compact groups $H$ and $K$ on a $C$^*$$-algebra.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Karigiannis:2005:DS, author = "Spiro Karigiannis", title = "Deformations of {$G_2$} and {$\Spin(7)$} Structures", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1012--1055", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-039-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider some deformations of $G$_2$$-structures on 7-manifolds. We discover a canonical way to deform a $G$_2$$-structure by a vector field in which the associated metric gets {``twisted''} in some way by the vector cross product. We present a system of partial differential equations for an unknown vector field $w$ whose solution would yield a manifold with holonomy $G$_2$$. Similarly we consider analogous constructions for $Spin(7)$-structures on 8-manifolds. Some of the results carry over directly, while others do not because of the increased complexity of the $Spin(7)$ case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ozawa:2005:HGA, author = "Narutaka Ozawa and Marc A. Rieffel", title = "Hyperbolic Group {$C^*$}-Algebras and Free-Product {$C^*$}-Algebras as Compact Quantum Metric Spaces", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1056--1079", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-040-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $ell$ be a length function on a group $G$, and let $M$_{ell}$$ denote the operator of pointwise multiplication by $ell$ on $ell$^2$ (G)$. Following Connes, $M$_{ell}$$ can be used as a {``Dirac''} operator for $C$_r^*$ (G)$. It defines a Lipschitz seminorm on $C$_r^*$ (G)$, which defines a metric on the state space of $C$_r^*$ (G)$. We show that if $G$ is a hyperbolic group and if $ell$ is a word-length function on $G$, then the topology from this metric coincides with the weak- $*$ topology (our definition of a {``compact quantum metric space''}). We show that a convenient framework is that of filtered $C$^*$$-algebras which satisfy a suitable {``Haagerup-type''} condition. We also use this framework to prove an analogous fact for certain reduced free products of $C$^*$$-algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pritsker:2005:GSM, author = "Igor E. Pritsker", title = "The {Gelfond--Schnirelman} Method in Prime Number Theory", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1080--1101", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-041-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The original Gelfond--Schnirelman method, proposed in 1936, uses polynomials with integer coefficients and small norms on $[0,1]$ to give a Chebyshev-type lower bound in prime number theory. We study a generalization of this method for polynomials in many variables. Our main result is a lower bound for the integral of Chebyshev's ${\psi}$-function, expressed in terms of the weighted capacity. This extends previous work of Nair and Chudnovsky, and connects the subject to the potential theory with external fields generated by polynomial-type weights. We also solve the corresponding potential theoretic problem, by finding the extremal measure and its support.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Weston:2005:PRF, author = "Tom Weston", title = "Power Residues of {Fourier} Coefficients of Modular Forms", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1102--1120", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-042-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let ${\rho} : G$_Q$ {\rightarrow} GL$_n$ (Q ell)$ be a motivic $ell$-adic Galois representation. For fixed $m > 1$ we initiate an investigation of the density of the set of primes $p$ such that the trace of the image of an arithmetic Frobenius at $p$ under ${\rho}$ is an $m$-th power residue modulo $p$. Based on numerical investigations with modular forms we conjecture (with Ramakrishna) that this density equals $1/m$ whenever the image of ${\rho}$ is open. We further conjecture that for such ${\rho}$ the set of these primes $p$ is independent of any set defined by Cebatorev-style Galois-theoretic conditions (in an appropriate sense). We then compute these densities for certain $m$ in the complementary case of modular forms of CM-type with rational Fourier coefficients; our proofs are a combination of the Cebatorev density theorem (which does apply in the CM case) and reciprocity laws applied to Hecke characters. We also discuss a potential application (suggested by Ramakrishna) to computing inertial degrees at $p$ in abelian extensions of imaginary quadratic fields unramified away from $p$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Barr:2005:EEA, author = "Michael Barr and R. Raphael and R. G. Woods", title = "On {$\mathcal{CR}$}-epic Embeddings and Absolute {$\mathcal{CR}$}-epic Spaces", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1121--1138", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-043-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study Tychonoff spaces $X$ with the property that, for all topological embeddings $X {\rightarrow} Y$, the induced map $C(Y) {\rightarrow} C(X)$ is an epimorphism of rings. Such spaces are called absolute $mathcal(CR)-epic$. The simplest examples of $mathcal(CR)-epic$ spaces are \sigma-compact locally compact spaces and Lindel{\"o}f $P$-spaces. We show that $mathcal(CR)-epic$ first countable spaces must be locally compact. However, a {``bad''} class of $mathcal(CR)-epic$ spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not $mathcal(CR)-epic$ abound, and some are presented.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Burke:2005:MWE, author = "Maxim R. Burke and Arnold W. Miller", title = "Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense {Cantor} Set", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1139--1154", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-044-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set $A$ there exists a nowhere dense Cantor set $C$ such that $A cap C$ is nonmeager in $C$. We also examine variants of this result and establish a measure theoretic analog.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cojocaru:2005:SSL, author = "Alina Carmen Cojocaru and Etienne Fouvry and M. Ram Murty", title = "The Square Sieve and the {Lang--Trotter} Conjecture", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1155--1177", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-045-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $E$ be an elliptic curve defined over $\mathbb(Q)$ and without complex multiplication. Let $K$ be a fixed imaginary quadratic field. We find nontrivial upper bounds for the number of ordinary primes $p {\leq} x$ for which $\mathbb(Q)({\pi}$_p$) = K$, where ${\pi}$_p$$ denotes the Frobenius endomorphism of $E$ at $p$. More precisely, under a generalized Riemann hypothesis we show that this number is $O$_E$ (x$^{17{\SGMLfrasl}18}$ log x)$, and unconditionally we show that this number is $O$_{E, K}$ (x(log log x)$^{13{\SGMLfrasl}12}$ {\SGMLfrasl} (log x)$^{25{\SGMLfrasl}24}$)$. We also prove that the number of imaginary quadratic fields $K$, with $-\disc K {\leq} x$ and of the form $K = \mathbb(Q)({\pi}$_p$)$, is $ > > $_E$ logloglog x$ for $x {\geq} x$_0$ (E)$. These results represent progress towards a 1976 Lang--Trotter conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cutkosky:2005:ABL, author = "Steven Dale Cutkosky and Huy T{\`a}i H{\`a} and Hema Srinivasan and Emanoil Theodorescu", title = "Asymptotic Behavior of the Length of Local Cohomology", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1178--1192", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-046-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $k$ be a field of characteristic 0, $R = k[x$_1$, ldots, x$_d$ ]$ be a polynomial ring, and $m$ its maximal homogeneous ideal. Let $I subset R$ be a homogeneous ideal in $R$. Let ${\lambda}(M)$ denote the length of an $R$-module $M$. In this paper, we show that $lim$_{n {\rightarrow} {\infty}}$ {\lambda}(H$^0_{\mathfrak{m}}$ (R/I$^n$)) / n$^d$ = lim$_{n {\rightarrow} {\infty} {\lambda} (Ext$^d$ R}$ (R/I$^n$,R(-d))) / n$^d$$ always exists. This limit has been shown to be $e(I)/d!$ for $m$-primary ideals $I$ in a local Cohen--Macaulay ring, where $e(I)$ denotes the multiplicity of $I$. But we find that this limit may not be rational in general. We give an example for which the limit is an irrational number thereby showing that the lengths of these extention modules may not have polynomial growth.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dungey:2005:SCD, author = "Nick Dungey", title = "Some Conditions for Decay of Convolution Powers and Heat Kernels on Groups", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1193--1214", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-047-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a function on a unimodular locally compact group $G$, and denote by $K$_n$ = K*K* ... * K$ the $n$-th convolution power of $K$. Assuming that $K$ satisfies certain operator estimates in $L$^2$ (G)$, we give estimates of the norms $|K$_n$ |$_2$$ and $|K$_n$ |$_{{\infty}}$$ for large $n$. In contrast to previous methods for estimating $|K$_n$ |$_{{\infty}}$$, we do not need to assume that the function $K$ is a probability density or non-negative. Our results also adapt for continuous time semigroups on $G$. Various applications are given, for example, to estimates of the behaviour of heat kernels on Lie groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Khare:2005:RLC, author = "Chandrashekhar Khare", title = "Reciprocity Law for Compatible Systems of {Abelian} $\bmod p$ {Galois} Representations", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1215--1223", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-048-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The main result of the paper is a $reciprocity law$ which proves that compatible systems of semisimple, abelian mod $p$ representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the last section analogs for Galois groups of function fields of these results are explored, and a question is raised whose answer seems to require developments in transcendence theory in characteristic $p$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kopotun:2005:CPA, author = "K. A. Kopotun and D. Leviatan and I. A. Shevchuk", title = "Convex Polynomial Approximation in the Uniform Norm: Conclusion", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1224--1248", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-049-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Estimating the degree of approximation in the uniform norm, of a convex function on a finite interval, by convex algebraic polynomials, has received wide attention over the last twenty years. However, while much progress has been made especially in recent years by, among others, the authors of this article, separately and jointly, there have been left some interesting open questions. In this paper we give final answers to all those open problems. We are able to say, for each $r$ th differentiable convex function, whether or not its degree of convex polynomial approximation in the uniform norm may be estimated by a Jackson-type estimate involving the weighted Ditzian-Totik $k$ th modulus of smoothness, and how the constants in this estimate behave. It turns out that for some pairs $(k,r)$ we have such estimate with constants depending only on these parameters. For other pairs the estimate is valid, but only with constants that depend on the function being approximated, while there are pairs for which the Jackson-type estimate is, in general, invalid.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lindstrom:2005:SSC, author = "Mikael Lindstr{\"o}m and Eero Saksman and Hans-Olav Tylli", title = "Strictly Singular and Cosingular Multiplications", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1249--1278", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-050-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $L(X)$ be the space of bounded linear operators on the Banach space $X$. We study the strict singularity and cosingularity of the two-sided multiplication operators $S mapsto ASB$ on $L(X)$, where $A,B \in L(X)$ are fixed bounded operators and $X$ is a classical Banach space. Let $1 < p < {\infty}$ and $p {\not=} 2$. Our main result establishes that the multiplication $S mapsto ASB$ is strictly singular on $L(L^p (0,1))$ if and only if the non-zero operators $A, B \in L(L^p (0,1))$ are strictly singular. We also discuss the case where $X$ is a $mathcal{L}$^1$$- or a $mathcal{L}$^{{\infty}}$$-space, as well as several other relevant examples.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Maad:2005:SPH, author = "Sara Maad", title = "A Semilinear Problem for the {Heisenberg} {Laplacian} on Unbounded Domains", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1279--1290", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-051-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the semilinear equation - \Delta$_{\mathbb H}$ u({\eta}) + u({\eta}) = f({\eta}, u({\eta})), u \in S$^2_1$ ({\Omega}), where ${\Omega}$ is an unbounded domain of the Heisenberg group $\mathbb H$^N$$, $N {\geq} 1$. The space $S$^2_1$ ({\Omega})$ is the Heisenberg analogue of the Sobolev space $W$_0^{1,2}$ ({\Omega})$. The function $f : \overline {\Omega} \times (\mathbb R) {\rightarrow} (\mathbb R)$ is supposed to be odd in $u$, continuous and satisfy some (superlinear but subcritical) growth conditions. The operator $\Delta$_{\mathbb H}$$ is the subelliptic Laplacian on the Heisenberg group. We give a condition on ${\Omega}$ which implies the existence of infinitely many solutions of the above equation. In the proof we rewrite the equation as a variational problem, and show that the corresponding functional satisfies the Palais--Smale condition. This might be quite surprising since we deal with domains which are far from bounded. The technique we use rests on a compactness argument and the maximum principle.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Riveros:2005:DH, author = "Carlos M. C. Riveros and Keti Tenenblat", title = "{Dupin} Hypersurfaces in {$\mathbb R^5$}", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1291--1313", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-052-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study Dupin hypersurfaces in $\mathbb R$^5$$ parametrized by lines of curvature, with four distinct principal curvatures. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. We show that these vector valued functions are invariant by inversions and homotheties.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhitomirskii:2005:RDT, author = "M. Zhitomirskii", title = "Relative {Darboux} Theorem for Singular Manifolds and Local Contact Algebra", journal = j-CAN-J-MATH, volume = "57", number = "??", pages = "1314--1340", month = "????", year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-053-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In 1999 V. Arnol'd introduced the local contact algebra: studying the problem of classification of singular curves in a contact space, he showed the existence of the ghost of the contact structure (invariants which are not related to the induced structure on the curve). Our main result implies that the only reason for existence of the local contact algebra and the ghost is the difference between the geometric and (defined in this paper) algebraic restriction of a 1-form to a singular submanifold. We prove that a germ of any subset $N$ of a contact manifold is well defined, up to contactomorphisms, by the algebraic restriction to $N$ of the contact structure. This is a generalization of the Darboux-Givental' theorem for smooth submanifolds of a contact manifold. Studying the difference between the geometric and the algebraic restrictions gives a powerful tool for classification of stratified submanifolds of a contact manifold. This is illustrated by complete solution of three classification problems, including a simple explanation of V. Arnold's results and further classification results for singular curves in a contact space. We also prove several results on the external geometry of a singular submanifold $N$ in terms of the algebraic restriction of the contact structure to $N$. In particular, the algebraic restriction is zero if and only if $N$ is contained in a smooth Legendrian submanifold of $M$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2005:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2005 --- pour 2005", journal = j-CAN-J-MATH, volume = "57", number = "6", pages = "1341--1344", month = dec, year = "2005", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2005-054-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:12 MDT 2011", bibsource = "http://cms.math.ca/cjm/v57/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Said:2006:FEZ, author = "Salem Ben Sa{\"\i}d", title = "The Functional Equation of Zeta Distributions Associated With Non-{Euclidean} {Jordan} Algebras", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "3--22", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-001-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper is devoted to the study of certain zeta distributions associated with simple non-Euclidean Jordan algebras. An explicit form of the corresponding functional equation and Bernstein-type identities is obtained.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dabbaghian-Abdoly:2006:CRF, author = "Vahid Dabbaghian-Abdoly", title = "Constructing Representations of Finite Simple Groups and Covers", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "23--38", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-002-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a finite group and $chi$ be an irreducible character of $G$. An efficient and simple method to construct representations of finite groups is applicable whenever $G$ has a subgroup $H$ such that $chi$_H$$ has a linear constituent with multiplicity 1. In this paper we show (with a few exceptions) that if $G$ is a simple group or a covering group of a simple group and $chi$ is an irreducible character of $G$ of degree less than 32, then there exists a subgroup $H$ (often a Sylow subgroup) of $G$ such that $chi$_H$$ has a linear constituent with multiplicity 1.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Exel:2006:AID, author = "R. Exel and A. Vershik", title = "{$C^*$}-Algebras of Irreversible Dynamical Systems", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "39--63", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-003-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We show that certain $C$^*$$-algebras which have been studied by, among others, Arzumanian, Vershik, Deaconu, and Renault, in connection with a measure-preserving transformation of a measure space or a covering map of a compact space, are special cases of the endomorphism crossed-product construction recently introduced by the first named author. As a consequence these algebras are given presentations in terms of generators and relations. These results come as a consequence of a general theorem on faithfulness of representations which are covariant with respect to certain circle actions. For the case of topologically free covering maps we prove a stronger result on faithfulness of representations which needs no covariance. We also give a necessary and sufficient condition for simplicity.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Filippakis:2006:MRN, author = "Michael Filippakis and Leszek Gasi{\'n}ski and Nikolaos S. Papageorgiou", title = "Multiplicity Results for Nonlinear {Neumann} Problems", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "64--92", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-004-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we study nonlinear elliptic problems of Neumann type driven by the $p$-Laplacian differential operator. We look for situations guaranteeing the existence of multiple solutions. First we study problems which are strongly resonant at infinity at the first (zero) eigenvalue. We prove five multiplicity results, four for problems with nonsmooth potential and one for problems with a $C$^1$$-potential. In the last part, for nonsmooth problems in which the potential eventually exhibits a strict super- $p$-growth under a symmetry condition, we prove the existence of infinitely many pairs of nontrivial solutions. Our approach is variational based on the critical point theory for nonsmooth functionals. Also we present some results concerning the first two elements of the spectrum of the negative $p$-Laplacian with Neumann boundary condition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gordon:2006:MHM, author = "Julia Gordon", title = "{Motivic} {Haar} Measure on Reductive Groups", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "93--114", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-005-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We define a motivic analogue of the Haar measure for groups of the form $G(k((t)))$, where $k$ is an algebraically closed field of characteristic zero, and $G$ is a reductive algebraic group defined over $k$. A classical Haar measure on such groups does not exist since they are not locally compact. We use the theory of motivic integration introduced by M. Kontsevich to define an additive function on a certain natural Boolean algebra of subsets of $G(k((t)))$. This function takes values in the so-called dimensional completion of the Grothendieck ring of the category of varieties over the base field. It is invariant under translations by all elements of $G(k((t)))$, and therefore we call it a motivic analogue of Haar measure. We give an explicit construction of the motivic Haar measure, and then prove that the result is independent of all the choices that are made in the process.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ivorra:2006:QRE, author = "W. Ivorra and A. Kraus", title = "Quelques r{\'e}sultats sur les {\'e}quations $ax^p + by^p = cz^2$. ({French}) [{Some} results for the equations $ax^p + by^p = cz^2$]", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "115--153", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-006-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $p$ be a prime number ${\geq} 5$ and $a, b, c$ be non zero natural numbers. Using the works of K. Ribet and A. Wiles on the modular representations, we get new results about the description of the primitive solutions of the diophantine equation $ax^p + by^p = cz$^2$$, in case the product of the prime divisors of $abc$ divides $2 ell$, with $ell$ an odd prime number. For instance, under some conditions on $a, b, c$, we provide a constant $f(a,b,c)$ such that there are no such solutions if $p > f(a,b,c)$. In application, we obtain information concerning the $\mathbb Q$-rational points of hyperelliptic curves given by the equation $y$^2$ = x^p + d$ with $d \in {\mathbb Z}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Prestini:2006:SIP, author = "Elena Prestini", title = "Singular Integrals on Product Spaces Related to the {Carleson} Operator", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "154--179", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-007-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove $L^p (\mathbb T$^2$)$ boundedness, $1 < p {\leq} 2$, of variable coefficients singular integrals that generalize the double Hilbert transform and present two phases that may be of very rough nature. These operators are involved in problems of a.e. convergence of double Fourier series, likely in the role played by the Hilbert transform in the proofs of a.e. convergence of one dimensional Fourier series. The proof due to C.Fefferman provides a basis for our method.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Reiten:2006:IDR, author = "Idun Reiten and Claus Michael Ringel", title = "Infinite Dimensional Representations of Canonical Algebras", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "180--224", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-008-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with canonical algebras. The investigation is centered around the generic and the Pr{\"u}fer modules, and how other modules are determined by these modules.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Azam:2006:GRL, author = "Saeid Azam", title = "Generalized Reductive {Lie} Algebras: Connections With Extended Affine {Lie} Algebras and {Lie} Tori", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "225--248", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-009-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate a class of Lie algebras which we call $generalized reductive Lie algebras$. These are generalizations of semi-simple, reductive, and affine Kac--Moody Lie algebras. A generalized reductive Lie algebra which has an irreducible root system is said to be $irreducible$ and we note that this class of algebras has been under intensive investigation in recent years. They have also been called $extended affine Lie algebras$. The larger class of generalized reductive Lie algebras has not been so intensively investigated. We study them in this paper and note that one way they arise is as fixed point subalgebras of finite order automorphisms. We show that the core modulo the center of a generalized reductive Lie algebra is a direct sum of centerless Lie tori. Therefore one can use the results known about the classification of centerless Lie tori to classify the cores modulo centers of generalized reductive Lie algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hernandez:2006:CFP, author = "M. Bello Hern{\'a}ndez and J. M{\'\i}nguez Ceniceros", title = "Convergence of {Fourier--Pad{\'e}} Approximants for {Stieltjes} Functions", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "249--261", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-010-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove convergence of diagonal multipoint Pad{\'e} approximants of Stieltjes-type functions when a certain moment problem is determinate. This is used for the study of the convergence of Fourier--Pad{\'e} and nonlinear Fourier--Pad{\'e} approximants for such type of functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Biswas:2006:CPP, author = "Indranil Biswas", title = "Connections on a Parabolic Principal Bundle Over a Curve", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "262--281", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-011-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The aim here is to define connections on a parabolic principal bundle. Some applications are given.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fels:2006:NRH, author = "M. E. Fels and A. G. Renner", title = "Non-reductive Homogeneous Pseudo-{Riemannian} Manifolds of Dimension Four", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "282--311", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-012-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A method, due to {\'E}lie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with $(2,2)$ signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is simply connected, then it is shown to be diffeomorphic to ${\mathbb R}$^4$$. All metrics for the simply connected non-reductive Einstein spaces are given explicitly. There are no non-reductive pseudo-Riemannian homogeneous spaces of dimension two and none of dimension three with connected isotropy subgroup.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gamblin:2006:PIR, author = "Didier Gamblin", title = "Partie imaginaire des r{\'e}sonances de {Rayleigh} dans le cas d'une boule. ({French}) [{Imaginary} part of {Rayleigh} resonances in the case of a ball]", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "312--343", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-013-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Nous {\'e}tudions les r{\'e}sonances de Rayleigh cr{\'e}{\'e}es par une boule en dimension deux et trois. Nous savons qu'elles convergent exponentiellement vite vers l'axe r{\'e}el. Nous calculons exactement les fonctions r{\'e}sonantes associ{\'e}es puis nous les estimons asymptotiquement en fonction de la partie r{\'e}elle des r{\'e}sonances. L'application de la formule de Green nous donne alors le taux de d{\'e}croissance exponentielle de la partie imaginaire des r{\'e}sonances.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Goldberg:2006:RGE, author = "David Goldberg", title = "Reducibility for {$SU_n$} and Generic Elliptic Representations", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "344--361", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-014-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study reducibility of representations parabolically induced from discrete series representations of $SU$_n$ (F)$ for $F$ a $p$-adic field of characteristic zero. We use the approach of studying the relation between $R$-groups when a reductive subgroup of a quasi-split group and the full group have the same derived group. We use restriction to show the quotient of $R$-groups is in natural bijection with a group of characters. Applying this to $SU$_n$ (F) subset U$_n$ (F)$ we show the $R$ group for $SU$_n$$ is the semidirect product of an $R$-group for $U$_n$ (F)$ and this group of characters. We derive results on non-abelian $R$-groups and generic elliptic representations as well.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Goldin:2006:CPS, author = "R. F. Goldin and S. Martin", title = "Cohomology Pairings on the Symplectic Reduction of Products", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "362--380", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-015-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $M$ be the product of two compact Hamiltonian $T$-spaces $X$ and $Y$. We present a formula for evaluating integrals on the symplectic reduction of $M$ by the diagonal $T$ action. At every regular value of the moment map for $X times Y$, the integral is the convolution of two distributions associated to the symplectic reductions of $X$ by $T$ and of $Y$ by $T$. Several examples illustrate the computational strength of this relationship. We also prove a linear analogue which can be used to find cohomology pairings on toric orbifolds.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jakobson:2006:EMF, author = "Dmitry Jakobson and Nikolai Nadirashvili and Iosif Polterovich", title = "Extremal Metric for the First Eigenvalue on a {Klein} Bottle", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "381--400", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-016-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called extremal metrics. The only known extremal metrics are a round sphere, a standard projective plane, a Clifford torus and an equilateral torus. We construct an extremal metric on a Klein bottle. It is a metric of revolution, admitting a minimal isometric embedding into a sphere ${\mathbb S}$^4$$ by the first eigenfunctions. Also, this Klein bottle is a bipolar surface for Lawson's $tau$_{3,1}$$-torus. We conjecture that an extremal metric for the first eigenvalue on a Klein bottle is unique, and hence it provides a sharp upper bound for $lambda$_1$$ on a Klein bottle of a given area. We present numerical evidence and prove the first results towards this conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kolountzakis:2006:PEP, author = "Mihail N. Kolountzakis and Szil{\'a}rd Gy. R{\'e}v{\'e}sz", title = "On Pointwise Estimates of Positive Definite Functions With Given Support", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "401--418", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-017-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The following problem has been suggested by Paul Tur{\'a}n. Let $\Omega$ be a symmetric convex body in the Euclidean space ${\mathbb R}$^d$$ or in the torus ${\mathbb T}$^d$$. Then, what is the largest possible value of the integral of positive definite functions that are supported in $\Omega$ and normalized with the value 1 at the origin? From this, Arestov, Berdysheva and Berens arrived at the analogous pointwise extremal problem for intervals in ${\mathbb R}$. That is, under the same conditions and normalizations, the supremum of possible function values at $z$ is to be found for any given point $z \in \Omega$. However, it turns out that the problem for the real line has already been solved by Boas and Kac, who gave several proofs and also mentioned possible extensions to ${\mathbb R}$^d$$ and to non-convex domains as well. Here we present another approach to the problem, giving the solution in ${\mathbb R}$^d$$ and for several cases in ${\mathbb T}$^d$$. Actually, we elaborate on the fact that the problem is essentially one-dimensional and investigate non-convex open domains as well. We show that the extremal problems are equivalent to some more familiar ones concerning trigonometric polynomials, and thus find the extremal values for a few cases. An analysis of the relationship between the problem for ${\mathbb R}$^d$$ and that for ${\mathbb T}$^d$$ is given, showing that the former case is just the limiting case of the latter. Thus the hierarchy of difficulty is established, so that extremal problems for trigonometric polynomials gain renewed recognition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Snaith:2006:SCN, author = "Victor P. Snaith", title = "{Stark}'s Conjecture and New {Stickelberger} Phenomena", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "419--448", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-018-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce a new conjecture concerning the construction of elements in the annihilator ideal associated to a Galois action on the higher-dimensional algebraic $K$-groups of rings of integers in number fields. Our conjecture is motivic in the sense that it involves the (transcendental) Borel regulator as well as being related to $l$-adic {\'e}tale cohomology. In addition, the conjecture generalises the well-known Coates--Sinnott conjecture. For example, for a totally real extension when $r = -2, -4, -6, ...$ the Coates--Sinnott conjecture merely predicts that zero annihilates $K$_{-2r}$$ of the ring of $S$-integers while our conjecture predicts a non-trivial annihilator. By way of supporting evidence, we prove the corresponding (conjecturally equivalent) conjecture for the Galois action on the {\'e}tale cohomology of the cyclotomic extensions of the rationals.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Agarwal:2006:EMP, author = "Ravi P. Agarwal and Daomin Cao and Haishen L{\"u} and Donal O'Regan", title = "Existence and Multiplicity of Positive Solutions for Singular Semipositone $p$-{Laplacian} Equations", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "449--475", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-019-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Positive solutions are obtained for the boundary value problem -( | $u$ '|$^{p - 2}$ $u$ ')' = lambda $f$ ( $t$, $u$), $t$ \in (0, 1), $p$ > 1 $u$ (0) = $u$ (1) = 0. Here $f$ ( $t$, $u$) \geq - $M$, ( $M$ is a positive constant) for ( $t$, $u$) \in [0,1] x (0, \infty). We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chipalkatti:2006:ASA, author = "Jaydeep Chipalkatti", title = "Apolar Schemes of Algebraic Forms", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "476--491", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-020-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This is a note on the classical Waring's problem for algebraic forms. Fix integers $(n,d,r,s)$, and let $Lambda$ be a general $r$-dimensional subspace of degree $d$ homogeneous polynomials in $n + 1$ variables. Let $mathcal{A}$ denote the variety of $s$-sided polar polyhedra of $Lambda$. We carry out a case-by-case study of the structure of $mathcal{A}$ for several specific values of $(n,d,r,s)$. In the first batch of examples, $mathcal{A}$ is shown to be a rational variety. In the second batch, $mathcal{A}$ is a finite set of which we calculate the cardinality.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chua:2006:ETW, author = "Seng-Kee Chua", title = "Extension Theorems on Weighted {Sobolev} Spaces and Some Applications", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "492--528", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-021-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We extend the extension theorems to weighted Sobolev spaces $L$^p_{w,k}$ (\mathcal D)$ on $(varepsilon, \delta)$ domains with doubling weight $w$ that satisfies a Poincar{\'e} inequality and such that $w$^{-1/p}$$ is locally $L$^{p'}$$. We also make use of the main theorem to improve weighted Sobolev interpolation inequalities.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dijkstra:2006:GHR, author = "Jan J. Dijkstra and Jan van Mill", title = "On the Group of Homeomorphisms of the Real Line That Map the Pseudoboundary Onto Itself", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "529--547", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-022-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we primarily consider two natural subgroups of the autohomeomorphism group of the real line $\mathbb{R}$, endowed with the compact-open topology. First, we prove that the subgroup of homeomorphisms that map the set of rational numbers $\mathbb{Q}$ onto itself is homeomorphic to the infinite power of $\mathbb{Q}$ with the product topology. Secondly, the group consisting of homeomorphisms that map the pseudoboundary onto itself is shown to be homeomorphic to the hyperspace of nonempty compact subsets of $\mathbb{Q}$ with the Vietoris topology. We obtain similar results for the Cantor set but we also prove that these results do not extend to $\mathbb{R}$^n$$ for $n geq 2$, by linking the groups in question with Erd{\"o}s space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Galanopoulos:2006:HQH, author = "P. Galanopoulos and M. Papadimitrakis", title = "{Hausdorff} and Quasi-{Hausdorff} Matrices on Spaces of Analytic Functions", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "548--579", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-023-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and BMOA. When the generating sequence of the matrix is the moment sequence of a measure $mu$, we find the conditions on $mu$ which are equivalent to the boundedness of the matrix on the various spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Greither:2006:ACG, author = "Cornelius Greither and Radan Kucera", title = "Annihilators for the Class Group of a Cyclic Field of Prime Power Degree, {II}", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "580--599", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-024-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove, for a field $K$ which is cyclic of odd prime power degree over the rationals, that the annihilator of the quotient of the units of $K$ by a suitable large subgroup (constructed from circular units) annihilates what we call the non-genus part of the class group. This leads to stronger annihilation results for the whole class group than a routine application of the Rubin--Thaine method would produce, since the part of the class group determined by genus theory has an obvious large annihilator which is not detected by that method; this is our reason for concentrating on the non-genus part. The present work builds on and strengthens previous work of the authors; the proofs are more conceptual now, and we are also able to construct an example which demonstrates that our results cannot be easily sharpened further.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Martinez-Maure:2006:GSM, author = "Yves Martinez-Maure", title = "Geometric Study of {Minkowski} Differences of Plane Convex Bodies", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "600--624", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-025-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In the Euclidean plane $\mathbb{R}$^2$$, we define the Minkowski difference $mathcal{K} - mathcal{L}$ of two arbitrary convex bodies $mathcal{K}$, $mathcal{L}$ as a rectifiable closed curve $mathcal{H}$_h$ \subset \mathbb{R}$^2$$ that is determined by the difference $h = h$_{mathcal{K}}$- h$_{mathcal{L}}$$ of their support functions. This curve $mathcal{H}$_h$$ is called the hedgehog with support function $h$. More generally, the object of hedgehog theory is to study the Brunn--Minkowski theory in the vector space of Minkowski differences of arbitrary convex bodies of Euclidean space $\mathbb{R}$^{n + 1}$$, defined as (possibly singular and self-intersecting) hypersurfaces of $\mathbb{R}$^{n + 1}$$. Hedgehog theory is useful for: (i) studying convex bodies by splitting them into a sum in order to reveal their structure; (ii) converting analytical problems into geometrical ones by considering certain real functions as support functions. The purpose of this paper is to give a detailed study of plane hedgehogs, which constitute the basis of the theory. In particular: (i) we study their length measures and solve the extension of the Christoffel--Minkowski problem to plane hedgehogs; (ii) we characterize support functions of plane convex bodies among support functions of plane hedgehogs and support functions of plane hedgehogs among continuous functions; (iii) we study the mixed area of hedgehogs in $\mathbb{R}$^2$$ and give an extension of the classical Minkowski inequality (and thus of the isoperimetric inequality) to hedgehogs.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mohrdieck:2006:SCS, author = "Stephan Mohrdieck", title = "A {Steinberg} Cross Section for Non-Connected Affine {Kac--Moody} Groups", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "625--642", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-026-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we generalise the concept of a Steinberg cross section to non-connected affine Kac--Moody groups. This Steinberg cross section is a section to the restriction of the adjoint quotient map to a given exterior connected component of the affine Kac--Moody group. (The adjoint quotient is only defined on a certain submonoid of the entire group, however, the intersection of this submonoid with each connected component is non-void.) The image of the Steinberg cross section consists of a {``twisted Coxeter cell''}, a transversal slice to a twisted Coxeter element. A crucial point in the proof of the main result is that the image of the cross section can be endowed with a $\mathbb{C}$^*$$-action.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yu:2006:CTC, author = "Xiaoxiang Yu", title = "Centralizers and Twisted Centralizers: Application to Intertwining Operators", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "643--672", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-027-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The equality of the centralizer and twisted centralizer is proved based on a case-by-case analysis when the unipotent radical of a maximal parabolic subgroup is abelian. Then this result is used to determine the poles of intertwining operators.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bart:2006:GCC, author = "Anneke Bart and Kevin P. Scannell", title = "The Generalized Cuspidal Cohomology Problem", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "673--690", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-028-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\Gamma \subset {\mathbb SO}(3,1)$ be a lattice. The well known $bending deformations$, introduced by linebreak Thurston and Apanasov, can be used to construct non-trivial curves of representations of $\Gamma$ into ${\mathbb SO}(4,1)$ when $\Gamma \backslash H$^3$$ contains an embedded totally geodesic surface. A tangent vector to such a curve is given by a non-zero group cohomology class in $H$^1$ (\Gamma, R$^4_1$)$. Our main result generalizes this construction of cohomology to the context of {``branched''} totally geodesic surfaces. We also consider a natural generalization of the famous cuspidal cohomology problem for the Bianchi groups (to coefficients in non-trivial representations), and perform calculations in a finite range. These calculations lead directly to an interesting example of a link complement in $S$^3$$ which is not infinitesimally rigid in ${\mathbb SO}(4,1)$. The first order deformations of this link complement are supported on a piecewise totally geodesic 2-complex.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bendikov:2006:HBI, author = "A. Bendikov and L. Saloff-Coste", title = "Hypoelliptic Bi-Invariant {Laplacians} on Infinite Dimensional Compact Groups", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "691--725", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-029-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "On a compact connected group $G$, consider the infinitesimal generator $-L$ of a central symmetric Gaussian convolution semigroup $(mu$_t$)$_{t > 0}$$. Using appropriate notions of distribution and smooth function spaces, we prove that $L$ is hypoelliptic if and only if $(mu$_t$)$_{t > 0}$$ is absolutely continuous with respect to Haar measure and admits a continuous density $x \mapsto mu$_t$ (x)$, $t > 0$, such that $lim$_{t rightarrow 0}$ t log mu$_t$ (e) = 0$. In particular, this condition holds if and only if any Borel measure $u$ which is solution of $Lu = 0$ in an open set $\Omega$ can be represented by a continuous function in $\Omega$. Examples are discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chiang:2006:VDT, author = "Yik-Man Chiang and Mourad E. H. Ismail", title = "On Value Distribution Theory of Second Order Periodic {ODE}s, Special Functions and Orthogonal Polynomials", journal = j-CAN-J-MATH, volume = "58", number = "4", pages = "726--767", month = aug, year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-030-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{Chiang:2010:EVD}.", abstract = "We show that the value distribution (complex oscillation) of solutions of certain periodic second order ordinary differential equations studied by Bank, Laine and Langley is closely related to confluent hypergeometric functions, Bessel functions and Bessel polynomials. As a result, we give a complete characterization of the zero-distribution in the sense of Nevanlinna theory of the solutions for two classes of the ODEs. Our approach uses special functions and their asymptotics. New results concerning finiteness of the number of zeros (finite-zeros) problem of Bessel and Coulomb wave functions with respect to the parameters are also obtained as a consequence. We demonstrate that the problem for the remaining class of ODEs not covered by the above {``special function approach''} can be described by a classical Heine problem for differential equations that admit polynomial solutions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hu:2006:DNA, author = "Zhiguo Hu and Matthias Neufang", title = "Decomposability of {von Neumann} Algebras and the {Mazur} Property of Higher Level", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "768--795", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-031-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The decomposability number of a von Neumann algebra $\cal M$ (denoted by $dec(\cal M)$) is the greatest cardinality of a family of pairwise orthogonal non-zero projections in $\cal M$. In this paper, we explore the close connection between $dec(\cal M)$ and the cardinal level of the Mazur property for the predual $\cal M$_*$$ of $\cal M$, the study of which was initiated by the second author. Here, our main focus is on those von Neumann algebras whose preduals constitute such important Banach algebras on a locally compact group $G$ as the group algebra $L$_1$ (G)$, the Fourier algebra $A(G)$, the measure algebra $M(G)$, the algebra $LUC(G)$^*$$, etc. We show that for any of these von Neumann algebras, say $\cal M$_0$$, the cardinal number $dec(\cal M)$ and a certain cardinal level of the Mazur property of $(cal M)$_*$$ are completely encoded in the underlying group structure. In fact, they can be expressed precisely by two dual cardinal invariants of $G$: the compact covering number $$_{\cal K}$ (G)$ of $G$ and the least cardinality $$_{\cal X}$ (G)$ of an open basis at the identity of $G$. We also present an application of the Mazur property of higher level to the topological centre problem for the Banach algebra $A(G)$^{**}$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Im:2006:MWG, author = "Bo-Hae Im", title = "{Mordell--Weil} Groups and the Rank of Elliptic Curves over Large Fields", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "796--819", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-032-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a number field, $\overline {K}$ an algebraic closure of $K$ and $E/K$ an elliptic curve defined over $K$. In this paper, we prove that if $E/K$ has a $K$-rational point $P$ such that $2P \neq O$ and $3P \neq O$, then for each $\sigma \in Gal(\overline {K}/K)$, the Mordell--Weil group $E(\overline {K}$^{\sigma}$)$ of $E$ over the fixed subfield of $\overline {K}$ under $\sigma$ has infinite rank.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Moreno:2006:DMC, author = "J. P. Moreno and P. L. Papini and R. R. Phelps", title = "Diametrically Maximal and Constant Width Sets in {Banach} Spaces", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "820--842", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-033-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We characterize diametrically maximal and constant width sets in $C(K)$, where $K$ is any compact Hausdorff space. These results are applied to prove that the sum of two diametrically maximal sets needs not be diametrically maximal, thus solving a question raised in a paper by Groemer. A characterization of diametrically maximal sets in $ell$_1^3$$ is also given, providing a negative answer to Groemer's problem in finite dimensional spaces. We characterize constant width sets in $c$_0$ (I)$, for every $I$, and then we establish the connections between the Jung constant of a Banach space and the existence of constant width sets with empty interior. Porosity properties of families of sets of constant width and rotundity properties of diametrically maximal sets are also investigated. Finally, we present some results concerning non-reflexive and Hilbert spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ozluk:2006:OLD, author = "A. E. {\~O}zl{\"u}k and C. Snyder", title = "On the One-Level Density Conjecture for Quadratic {Dirichlet} {L}-Functions", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "843--858", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-034-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In a previous article, we studied the distribution of {``low-lying''} zeros of the family of quadratic Dirichlet $L$-functions assuming the Generalized Riemann Hypothesis for all Dirichlet $L$-functions. Even with this very strong assumption, we were limited to using weight functions whose Fourier transforms are supported in the interval $(-2,2)$. However, it is widely believed that this restriction may be removed, and this leads to what has become known as the One-Level Density Conjecture for the zeros of this family of quadratic $L$-functions. In this note, we make use of Weil's explicit formula as modified by Besenfelder to prove an analogue of this conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Read:2006:NIN, author = "C. J. Read", title = "Nonstandard Ideals from Nonstandard Dual Pairs for {{$L^1(\omega)$}} and $l^1(\omega)$", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "859--876", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-035-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Banach convolution algebras $l$^1$ (\omega)$ and their continuous counterparts $L$^1$ (\mathbb R$^+$, \omega)$ are much studied, because (when the submultiplicative weight function $\omega$ is radical) they are pretty much the prototypic examples of commutative radical Banach algebras. In cases of {``nice''} weights $\omega$, the only closed ideals they have are the obvious, or {``standard''}, ideals. But in the general case, a brilliant but very difficult paper of Marc Thomas shows that nonstandard ideals exist in $l$^1$ (\omega)$. His proof was successfully exported to the continuous case $L$^1$ (\mathbb R$^+$, \omega)$ by Dales and McClure, but remained difficult. In this paper we first present a small improvement: a new and easier proof of the existence of nonstandard ideals in $l$^1$ (\omega)$ and $L$^1$ (\mathbb R$^+$, \omega)$. The new proof is based on the idea of a {``nonstandard dual pair''} which we introduce. We are then able to make a much larger improvement: we find nonstandard ideals in $L$^1$ (\mathbb R$^+$, \omega)$ containing functions whose supports extend all the way down to zero in $(\mathbb R$^+$)$, thereby solving what has become a notorious problem in the area.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Selick:2006:FDL, author = "P. Selick and S. Theriault and J. Wu", title = "Functorial Decompositions of Looped Coassociative Co-{$H$} Spaces", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "877--896", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-036-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Selick and Wu gave a functorial decomposition of $\Omega Sigma X$ for path-connected, $p$-local $CW$-complexes $X$ which obtained the smallest nontrivial functorial retract $A$^{min}$ (X)$ of $\Omega Sigma X$. This paper uses methods developed by the second author in order to extend such functorial decompositions to the loops on coassociative co- $H$ spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Courtes:2006:DIG, author = "Fran{\c{c}}ois Court{\`e}s", title = "Distributions invariantes sur les groupes r{\'e}ductifs quasi-d{\'e}ploy{\'e}s. ({French}) [{Invariant} distributions on quasi-deployed reductive groups]", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "897--999", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-037-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soit $F$ un corps local non archim{\'e}dien, et $G$ le groupe des $F$-points d'un groupe r{\'e}ductif connexe quasi-d{\'e}ploy{\'e} d{\'e}fini sur $F$. Dans cet article, on s'int{\'e}resse aux distributions sur $G$ invariantes par conjugaison, et {\`a} l'espace de leurs restrictions {\`a} l'alg{\`e}bre de Hecke \mathcal{H} des fonctions sur $G$ {\`a} support compact biinvariantes par un sous-groupe d'Iwahori $I$ donn{\'e}. On montre tout d'abord que les valeurs d'une telle distribution sur \mathcal{H} sont enti{\`e}rement d{\'e}termin{\'e}es par sa restriction au sous-espace de dimension finie des {\'e}l{\'e}ments de \mathcal{H} {\`a} support dans la r{\'e}union des sous-groupes parahoriques de $G$ contenant $I$. On utilise ensuite cette propri{\'e}t{\'e} pour montrer, moyennant certaines conditions sur $G$, que cet espace est engendr{\'e} d'une part par certaines int{\'e}grales orbitales semi-simples, d'autre part par les int{\'e}grales orbitales unipotentes, en montrant tout d'abord des r{\'e}sultats analogues sur les groupes finis.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Dhillon:2006:CMV, author = "Ajneet Dhillon", title = "On the Cohomology of Moduli of Vector Bundles and the {Tamagawa} Number of {$\SL_n$}", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1000--1025", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-038-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We compute some Hodge and Betti numbers of the moduli space of stable rank $r$, degree $d$ vector bundles on a smooth projective curve. We do not assume $r$ and $d$ are coprime. In the process we equip the cohomology of an arbitrary algebraic stack with a functorial mixed Hodge structure. This Hodge structure is computed in the case of the moduli stack of rank $r$, degree $d$ vector bundles on a curve. Our methods also yield a formula for the Poincar{\'e} polynomial of the moduli stack that is valid over any ground field. In the last section we use the previous sections to give a proof that the Tamagawa number of SL$_n$ is one.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Handelman:2006:KRL, author = "David Handelman", title = "{Karamata} Renewed and Local Limit Results", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1026--1094", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-039-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Connections between behaviour of real analytic functions (with no negative Maclaurin series coefficients and radius of convergence one) on the open unit interval, and to a lesser extent on arcs of the unit circle, are explored, beginning with Karamata's approach. We develop conditions under which the asymptotics of the coefficients are related to the values of the function near 1; specifically, a(n)\sim f(1-1/n)/ \alpha n (for some positive constant \alpha), where f(t)=\sum a(n)t$^n$. In particular, if F=\sum c(n) t$^n$ where c(n) \geq 0 and \sum c(n)=1, then $f$ defined as (1-F)^{-1} (the renewal or Green's function for $F$) satisfies this condition if F' does (and a minor additional condition is satisfied). In come cases, we can show that the absolute sum of the differences of consecutive Maclaurin coefficients converges. We also investigate situations in which less precise asymptotics are available.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sakellaridis:2006:CSF, author = "Yiannis Sakellaridis", title = "A {Casselman--Shalika} Formula for the {Shalika} Model of {$\GL_n$}", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1095--1120", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-040-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Casselman--Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of $p$-adic groups that are associated to unique models (i.e., multiplicity-free induced representations). We apply this method to the case of the Shalika model of GL$_n$, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of the method, that was introduced by Y. Hironaka, and in effect reduce many such problems to straightforward calculations on the group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bownik:2006:FCW, author = "Marcin Bownik and Darrin Speegle", title = "The {Feichtinger} Conjecture for Wavelet Frames, {Gabor} Frames and Frames of Translates", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1121--1143", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-041-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hamana:2006:PAN, author = "Masamichi Hamana", title = "Partial $ * $-Automorphisms, Normalizers, and Submodules in Monotone Complete {$C^*$}-Algebras", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1144--1202", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-042-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For monotone complete $C$^*$$-algebras $A subset B$ with $A$ contained in $B$ as a monotone closed $C$^*$$-subalgebra, the relation $X = AsA$ gives a bijection between the set of all monotone closed linear subspaces $X$ of $B$ such that $AX + XA subset X$ and $XX$^*$ + X$^*$ X subset A$ and a set of certain partial isometries $s$ in the {``normalizer''} of $A$ in $B$, and similarly for the map $s mapsto$ Ad $s$ between the latter set and a set of certain {``partial $*$-automorphisms''} of $A$. We introduce natural inverse semigroup structures in the set of such $X$ 's and the set of partial $*$-automorphisms of $A$, modulo a certain relation, so that the composition of these maps induces an inverse semigroup homomorphism between them. For a large enough $B$ the homomorphism becomes surjective and all the partial $*$-automorphisms of $A$ are realized via partial isometries in $B$. In particular, the inverse semigroup associated with a type II $$_1$$ von Neumann factor, modulo the outer automorphism group, can be viewed as the fundamental group of the factor. We also consider the $C$^*$$-algebra version of these results.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Heiermann:2006:OUP, author = "Volker Heiermann", title = "Orbites unipotentes et p{\^o}les d'ordre maximal de la fonction $\mu$ de {Harish-Chandra}. ({French}) [{Unipotent} orbits and poles of maximal order of the {Harish-Chandra} $\mu$ function]", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1203--1228", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-043-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Dans un travail ant{\'e}rieur, nous avions montr{\'e} que l'induite parabolique (normalis{\'e}e) d'une repr{\'e}sentation irr{\'e}ductible cuspidale $\sigma$ d'un sous-groupe de Levi $M$ d'un groupe $p$-adique contient un sous-quotient de carr{\'e} int{\'e}grable, si et seulement si la fonction $mu$ de Harish-Chandra a un p{\^o}le en $\sigma$ d'ordre {\'e}gal au rang parabolique de $M$. L'objet de cet article est d'interpr{\'e}ter ce r{\'e}sultat en termes de fonctorialit{\'e} de Langlands.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Henniart:2006:IOT, author = "Guy Henniart and Bertrand Lemaire", title = "Int{\'e}grales orbitales tordues sur {$\GL(n, F)$} et corps locaux proches: applications. ({French}) [{Twisted} orbital integrals on {$\GL(n, F)$} and close local bodies: applications]", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1229--1267", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-044-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soient $F$ un corps commutatif localement compact non archim{\'e}dien, $G = GL (n,F)$ pour un entier $n geq 2$, et $kappa$ un caract{\`e}re de $F$^x$$ trivial sur $(F$^x$)$^n$$. On prouve une formule pour les $kappa$-int{\'e}grales orbitales r{\'e}guli{\`e}res sur $G$ permettant, si $F$ est de caract{\'e}ristique $ > 0$, de les relever {\`a} la caract{\'e}ristique nulle. On en d{\'e}duit deux r{\'e}sultats nouveaux en caract{\'e}ristique $ > 0$: le {``lemme fondamental''} pour l'induction automorphe, et une version simple de la formule des traces tordue locale d'Arthur reliant $kappa$-int{\'e}grales orbitales elliptiques et caract{\`e}res $kappa$-tordus. Cette formule donne en particulier, pour une s{\'e}rie $kappa$-discr{\`e}te de $G$, les $kappa$-int{\'e}grales orbitales elliptiques d'un pseudo-coefficient comme valeurs du caract{\`e}re $kappa$-tordu.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Sims:2006:GII, author = "Aidan Sims", title = "Gauge-Invariant Ideals in the {$C^*$}-Algebras of Finitely Aligned Higher-Rank Graphs", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1268--1290", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-045-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We produce a complete description of the lattice of gauge-invariant ideals in $C$^*$ (Lambda)$ for a finitely aligned $k$-graph $Lambda$. We provide a condition on $Lambda$ under which every ideal is gauge-invariant. We give conditions on $Lambda$ under which $C$^*$ (Lambda)$ satisfies the hypotheses of the Kirchberg--Phillips classification theorem.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Weimar-Woods:2006:GSG, author = "Evelyn Weimar-Woods", title = "The General Structure of {$G$}-Graded Contractions of {Lie} Algebras {I}. The Classification", journal = j-CAN-J-MATH, volume = "58", number = "??", pages = "1291--1340", month = "????", year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-046-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give the general structure of complex (resp., real) $G$-graded contractions of Lie algebras where $G$ is an arbitrary finite Abelian group. For this purpose, we introduce a number of concepts, such as pseudobasis, higher-order identities, and sign invariants. We characterize the equivalence classes of $G$-graded contractions by showing that our set of invariants (support, higher-order identities, and sign invariants) is complete, which yields a classification.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2006:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2006 --- pour 2006", journal = j-CAN-J-MATH, volume = "58", number = "6", pages = "1341--1344", month = dec, year = "2006", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2006-047-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Biller:2007:HGC, author = "Harald Biller", title = "Holomorphic Generation of Continuous Inverse Algebras", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "3--35", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-001-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixed $n$-tuple of elements are dense. In particular, we characterize the compact subsets of $(\mathbb C)$^n$$ which appear as joint spectra of such $n$-tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Develin:2007:CDS, author = "Mike Develin and Jeremy L. Martin and Victor Reiner", title = "Classification of {Ding}'s {Schubert} Varieties: Finer Rook Equivalence", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "36--62", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-002-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "K. Ding studied a class of Schubert varieties $X$_\lambda$$ in type A partial flag manifolds, indexed by integer partitions $lambda$ and in bijection with dominant permutations. He observed that the Schubert cell structure of $X$_\lambda$$ is indexed by maximal rook placements on the Ferrers board $B$_\lambda$$, and that the integral cohomology groups $H$^*$ (X$_\lambda$ (\mathbb Z))$, $H$^*$ (X$_\mu$ (\mathbb Z))$ are additively isomorphic exactly when the Ferrers boards $B$_\lambda$, B$_\mu$$ satisfy the combinatorial condition of $rook-equivalence$. We classify the varieties $X$_\lambda$$ up to isomorphism, distinguishing them by their graded cohomology rings with integer coefficients. The crux of our approach is studying the nilpotence orders of linear forms in the cohomology ring.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ferenczi:2007:SRS, author = "Valentin Ferenczi and El{\'o}i Medina Galego", title = "Some Results on the {Schroeder--Bernstein} Property for Separable {Banach} Spaces", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "63--84", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-003-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We construct a continuum of mutually non-isomorphic separable Banach spaces which are complemented in each other. Consequently, the Schroeder--Bernstein Index of any of these spaces is $2$^{aleph 0}$$. Our construction is based on a Banach space introduced by W. T. Gowers and B. Maurey in 1997. We also use classical descriptive set theory methods, as in some work of the first author and C. Rosendal, to improve some results of P. G. Casazza and of N. J. Kalton on the Schroeder--Bernstein Property for spaces with an unconditional finite-dimensional Schauder decomposition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Foster:2007:CCN, author = "J. H. Foster and Monika Serbinowska", title = "On the Convergence of a Class of Nearly Alternating Series", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "85--108", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-004-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $C$ be the class of convex sequences of real numbers. The quadratic irrational numbers can be partitioned into two types as follows. If $\alpha$ is of the first type and $(c$_k$) \in C$, then $\sum (-1)$^{lfloor k \alpha \rfloor}$ c$_k$$ converges if and only if $c$_k$ log k \rightarrow 0$. If $\alpha$ is of the second type and $(c$_k$) \in C$, then $\sum (-1)$^{lfloor k \alpha \rfloor}$ c$_k$$ converges if and only if $\sum c$_k$ /k$ converges. An example of a quadratic irrational of the first type is $\sqrt{2}$, and an example of the second type is $\sqrt{3}$. The analysis of this problem relies heavily on the representation of $\alpha$ as a simple continued fraction and on properties of the sequences of partial sums $S(n) = \sum$_{k=1}^n$ (-1)$^{lfloor k\alpha \rfloor}$$ and double partial sums $T(n) = \sum$_{k=1}^n$ S(k)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jayanthan:2007:FCP, author = "A. V. Jayanthan and Tony J. Puthenpurakal and J. K. Verma", title = "On Fiber Cones of $\mathfrak{m}$-Primary Ideals", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "109--126", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-005-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Two formulas for the multiplicity of the fiber cone $F(I) = bigoplus$_{n=0}^\infty$ I$^n$ / m I$^n$$ of an $m$-primary ideal of a $d$-dimensional Cohen--Macaulay local ring $(R,m)$ are derived in terms of the mixed multiplicity $e$_{d-1}$ (m | I)$, the multiplicity $e(I)$, and superficial elements. As a consequence, the Cohen--Macaulay property of $F(I)$ when $I$ has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of the reduction number of $I$ and lengths of certain ideals. We also characterize the Cohen--Macaulay and Gorenstein properties of fiber cones of $m$-primary ideals with a $d$-generated minimal reduction $J$ satisfying $ell(I$^2$ /JI) = 1$ or $ell(Im/Jm) = 1.$", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lamzouri:2007:SVI, author = "Youness Lamzouri", title = "Smooth Values of the Iterates of the {Euler} Phi-Function", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "127--147", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-006-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $phi(n)$ be the Euler phi-function, define $phi$_0$ (n) = n$ and $phi$_{k+1}$ (n) = phi(phi$_k$ (n))$ for all $k \geq 0$. We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $phi$_k$ (n)$. is $y$-smooth, conditionally on a weak form of the Elliott--Halberstam conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Muic:2007:CCU, author = "Goran Mui{\'c}", title = "On Certain Classes of Unitary Representations for Split Classical Groups", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "148--185", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-007-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we prove the unitarity of duals of tempered representations supported on minimal parabolic subgroups for split classical $p$-adic groups. We also construct a family of unitary spherical representations for real and complex classical groups", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Okoh:2007:EAK, author = "F. Okoh and F. Zorzitto", title = "Endomorphism Algebras of {Kronecker} Modules Regulated by Quadratic Function Fields", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "186--210", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-008-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Purely simple Kronecker modules $mathcal M$, built from an algebraically closed field $K$, arise from a triplet $(m,h, \alpha)$ where $m$ is a positive integer, $h: K \bigcup {\infty} \longrightarrow {\infty,0,1,2,3,dots}$ is a height function, and $\alpha$ is a $K$-linear functional on the space $K(X)$ of rational functions in one variable $X$. Every pair $(h, \alpha)$ comes with a polynomial $f$ in $K(X)[Y]$ called the regulator. When the module $mathcal M$ admits non-trivial endomorphisms, $f$ must be linear or quadratic in $Y$. In that case $mathcal M$ is purely simple if and only if $f$ is an irreducible quadratic. Then the $K$-algebra $End (\mathcal M)$ embeds in the quadratic function field $K(X)[Y]/(f)$. For some height functions $h$ of infinite support $I$, the search for a functional $\alpha$ for which $(h, \alpha)$ has regulator 0 comes down to having functions $eta : I longrightarrow K$ such that no planar curve intersects the graph of $eta$ on a cofinite subset. If $K$ has characterictic not 2, and the triplet $(m,h, \alpha)$ gives a purely-simple Kronecker module $mathcal M$ having non-trivial endomorphisms, then $h$ attains the value $\infty$ at least once on $K big cup {\infty}$ and $h$ is finite-valued at least twice on $K big cup {\infty}$. Conversely all these $h$ form part of such triplets. The proof of this result hinges on the fact that a rational function $r$ is a perfect square in $K(X)$ if and only if $r$ is a perfect square in the completions of $K(X)$ with respect to all of its valuations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Roy:2007:TEA, author = "Damien Roy", title = "On Two Exponents of Approximation Related to a Real Number and Its Square", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "211--224", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-009-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For each real number $xi$, let $lambdahat$_2$ (xi)$ denote the supremum of all real numbers $lambda$ such that, for each sufficiently large $X$, the inequalities $|x$_0$ | \leq X$, $|x$_0$ xi - x$_1$ | \leq X$^{-lambda}$$ and $|x$_0$ xi$^2$- x$_2$ | \leq X$^{-lambda}$$ admit a solution in integers $x$_0$$, $x$_1$$ and $x$_2$$ not all zero, and let $omegahat$_2$ (xi)$ denote the supremum of all real numbers $\omega$ such that, for each sufficiently large $X$, the dual inequalities $|x$_0$ + x$_1$ xi + x$_2$ xi$^2$ | \leq X$^{-\omega}$$, $|x$_1$ | \leq X$ and $|x$_2$ | \leq X$ admit a solution in integers $x$_0$$, $x$_1$$ and $x$_2$$ not all zero. Answering a question of Y. Bugeaud and M. Laurent, we show that the exponents $lambdahat$_2$ (xi)$ where $xi$ ranges through all real numbers with $[\mathbb Q(xi) : \mathbb Q] > 2$ form a dense subset of the interval $[1/2, (\sqrt{5} - 1)/2]$ while, for the same values of $xi$, the dual exponents $omegahat$_2$ (xi)$ form a dense subset of $[2, (\sqrt{5} + 3)/2]$. Part of the proof rests on a result of V. Jarnik showing that $lambdahat$_2$ (xi) = 1 - omegahat$_2$ (xi)$^{-1}$$ for any real number $xi$ with $[\mathbb Q(xi) : \mathbb Q] > 2$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baker:2007:HAM, author = "Matt Baker and Robert Rumely", title = "Harmonic Analysis on Metrized Graphs", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "225--275", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-010-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper studies the Laplacian operator on a metrized graph, and its spectral theory.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bernardis:2007:WIH, author = "A. L. Bernardis and F. J. Mart{\'\i}n-Reyes and P. Ortega Salvador", title = "Weighted Inequalities for {Hardy--Steklov} Operators", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "276--295", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-011-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We characterize the pairs of weights $(v,w)$ for which the operator $Tf(x) = g(x) \int$_{s(x)}^{h(x)}$ f$ with $s$ and $h$ increasing and continuous functions is of strong type $(p,q)$ or weak type $(p,q)$ with respect to the pair $(v,w)$ in the case $0 < q < p$ and $1 < p < \infty$. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon. In particular, we do not assume differentiability properties on $s$ and $h$ and we obtain that the strong type inequality $(p,q)$, $q < p$, is characterized by the fact that the function $Phi(x) = \sup (\int$_c^d$ g$^q$ w)$^{1/p}$ (\int$_{s(d)}^{h(c)}$ v$^{1-p'}$)$^{1/p'}$$ belongs to $L$^r$ (g$^q$ w)$, where $1/r = 1/q - 1/p$ and the supremum is taken over all $c$ and $d$ such that $c \leq x \leq d$ and $s(d) \leq h(c)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chein:2007:BLN, author = "Orin Chein and Edgar G. Goodaire", title = "Bol Loops of Nilpotence Class Two", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "296--310", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-012-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Call a non-Moufang Bol loop $minimally non-Moufang$ if every proper subloop is Moufang and $minimally nonassociative$ if every proper subloop is associative. We prove that these concepts are the same for Bol loops which are nilpotent of class two and in which certain associators square to 1. In the process, we derive many commutator and associator identities which hold in such loops.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Christianson:2007:GZZ, author = "Hans Christianson", title = "Growth and Zeros of the Zeta Function for Hyperbolic Rational Maps", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "311--331", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-013-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper describes new results on the growth and zeros of the Ruelle zeta function for the Julia set of a hyperbolic rational map. It is shown that the zeta function is bounded by $exp(C$_K$ |s|$^{\delta}$)$ in strips $|$ Re $s| \leq K$, where $\delta$ is the dimension of the Julia set. This leads to bounds on the number of zeros in strips (interpreted as the Pollicott--Ruelle resonances of this dynamical system). An upper bound on the number of zeros in polynomial regions ${|$ Re $s| \leq |$ Im $s|$^{\alpha}$}$ is given, followed by weaker lower bound estimates in strips ${$ Re $s > -C, |$ Im $s| \leq r}$, and logarithmic neighbourhoods ${|$ Re $s| \leq rho log |$ Im $s|}$. Recent numerical work of Strain--Zworski suggests the upper bounds in strips are optimal.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Leuschke:2007:ERF, author = "Graham J. Leuschke", title = "Endomorphism Rings of Finite Global Dimension", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "332--342", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-014-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a commutative local ring $R$, consider (noncommutative) $R$-algebras $Lambda$ of the form $Lambda =$ End $$_R$ (M)$ where $M$ is a reflexive $R$-module with nonzero free direct summand. Such algebras Lambda of finite global dimension can be viewed as potential substitutes for, or analogues of, a resolution of singularities of Spec $R$. For example, Van den Bergh has shown that a three-dimensional Gorenstein normal $\mathbb{C}$-algebra with isolated terminal singularities has a crepant resolution of singularities if and only if it has such an algebra $Lambda$ with finite global dimension and which is maximal Cohen--Macaulay over $R$ (a {``noncommutative crepant resolution of singularities''}). We produce algebras $Lambda =$ End $$_R$ (M)$ having finite global dimension in two contexts: when $R$ is a reduced one-dimensional complete local ring, or when $R$ is a Cohen--Macaulay local ring of finite Cohen--Macaulay type. If in the latter case $R$ is Gorenstein, then the construction gives a noncommutative crepant resolution of singularities in the sense of Van den Bergh.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lin:2007:WSP, author = "Huaxin Lin", title = "Weak Semiprojectivity in Purely Infinite Simple {$C^*$}-Algebras", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "343--371", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-015-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $A$ be a separable amenable purely infinite simple $C$^*$$-algebra which satisfies the Universal Coefficient Theorem. We prove that $A$ is weakly semiprojective if and only if $K$_i$ (A)$ is a countable direct sum of finitely generated groups ( $i = 0,1$). Therefore, if $A$ is such a $C$^*$$-algebra, for any $epsilon > 0$ and any finite subset ${mathcal F} subset A$ there exist $\delta > 0$ and a finite subset ${mathcal G} subset A$ satisfying the following: for any contractive positive linear map $L: A rightarrow B$ (for any $C$^*$$-algebra $B$) with $||L(ab) - L(a)L(b)|| < \delta$ for $a, b \in {mathcal G}$ there exists a homomorphism $h : A rightarrow B$ such that $||h(a) - L(a)|| < epsilon$ for $a \in {mathcal F}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Maisner:2007:ZFS, author = "Daniel Maisner and Enric Nart", title = "Zeta Functions of Supersingular Curves of Genus 2", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "372--392", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-016-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We determine which isogeny classes of supersingular abelian surfaces over a finite field $k$ of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to $k$-isomorphism, leading to the same zeta function.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Servat:2007:SPO, author = "E. Servat", title = "Le splitting pour l'op{\'e}rateur de {Klein--Gordon}: une approche heuristique et num{\'e}rique {Harish-Chandra}. ({French}) [{Splitting} for the {Klein--Gordon} operator: a heuristic numerical {Harish-Chandra} approach]", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "393--417", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-017-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Dans cet article on {\'e}tudie la diff{\'e}rence entre les deux premi{\`e}res valeurs propres, le splitting, d'un op{\'e}rateur de Klein--Gordon semi-classique unidimensionnel, dans le cas d'un potentiel sym{\'e}trique pr{\'e}sentant un double puits. Dans le cas d'une petite barri{\`e}re de potentiel, B. Helffer et B. Parisse ont obtenu des r{\'e}sultats analogues {\`a} ceux existant pour l'op{\'e}rateur de Schr{\"o}dinger. Dans le cas d'une grande barri{\`e}re de potentiel, on obtient ici des estimations des tranform{\'e}es de Fourier des fonctions propres qui conduisent {\`a} une conjecture du splitting. Des calculs num{\'e}riques viennent appuyer cette conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Stoimenow:2007:CKV, author = "A. Stoimenow", title = "On Cabled Knots and {Vassiliev} Invariants (Not) Contained in Knot Polynomials", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "418--448", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-018-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "It is known that the Brandt--Lickorish--Millett--Ho polynomial $Q$ contains Casson's knot invariant. Whether there are (essentially) other Vassiliev knot invariants obtainable from $Q$ is an open problem. We show that this is not so up to degree 9. We also give the (apparently) first examples of knots not distinguished by 2-cable HOMFLY polynomials which are not mutants. Our calculations provide evidence of a negative answer to the question whether Vassiliev knot invariants of degree $d \leq 10$ are determined by the HOMFLY and Kauffman polynomials and their 2-cables, and for the existence of algebras of such Vassiliev invariants not isomorphic to the algebras of their weight systems.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Badulescu:2007:ORT, author = "Alexandru Ioan Badulescu", title = "{$\SL_n$}, Orthogonality Relations and Transfer", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "449--464", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-019-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $pi$ be a square integrable representation of $G' =$ SL $$_n$ (D)$, with $D$ a central division algebra of finite dimension over a local field $F$ $of non-zero characteristic$. We prove that, on the elliptic set, the character of $pi$ equals the complex conjugate of the orbital integral of one of the pseudocoefficients of $pi$. We prove also the orthogonality relations for characters of square integrable representations of $G'$. We prove the stable transfer of orbital integrals between SL $$_n$ (F)$ and its inner forms.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Barr:2007:SAE, author = "Michael Barr and John F. Kennison and R. Raphael", title = "Searching for Absolute {$\mathcal{CR}$}-Epic Spaces", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "465--487", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-020-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In previous papers, Barr and Raphael investigated the situation of a topological space $Y$ and a subspace $X$ such that the induced map $C(Y) \to C(X)$ is an epimorphism in the category $(\mathcal CR)$ of commutative rings (with units). We call such an embedding a $(\mathcal CR)$-epic embedding and we say that $X$ is absolute $(\mathcal CR)$-epic if every embedding of $X$ is $(\mathcal CR)$-epic. We continue this investigation. Our most notable result shows that a Lindel{\"o}f space $X$ is absolute $(\mathcal CR)$-epic if a countable intersection of $\beta X$-neighbourhoods of $X$ is a $\beta X$-neighbourhood of $X$. This condition is stable under countable sums, the formation of closed subspaces, cozero-subspaces, and being the domain or codomain of a perfect map. A strengthening of the Lindel{\"o}f property leads to a new class with the same closure properties that is also closed under finite products. Moreover, all $\sigma$-compact spaces and all Lindel{\"o}f $P$-spaces satisfy this stronger condition. We get some results in the non-Lindel{\"o}f case that are sufficient to show that the Dieudonn{\'e} plank and some closely related spaces are absolute $(\mathcal CR)$-epic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bernardi:2007:OVV, author = "A. Bernardi and M. V. Catalisano and A. Gimigliano and M. Id{\`a}", title = "Osculating Varieties of {Veronese} Varieties and Their Higher Secant Varieties", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "488--502", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-021-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider the $k$-osculating varieties $O$_{k,n.d}$$ to the (Veronese) $d$-uple embeddings of $(\mathbb P)$^n$$. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes $Y \subset (\mathbb P)$^n$$ to $O$^s_{k,n,d}$$ and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chevallier:2007:CGT, author = "Nicolas Chevallier", title = "Cyclic Groups and the Three Distance Theorem", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "503--552", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-022-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give a two dimensional extension of the three distance Theorem. Let $\theta$ be in $(mathbf R)$^2$$ and let $q$ be in $(mathbf N)$. There exists a triangulation of $(mathbf R)$^2$$ invariant by $(mathbf Z)$^2$$-translations, whose set of vertices is $(mathbf Z)$^2$ + {0, \theta, dots, q \theta}$, and whose number of different triangles, up to translations, is bounded above by a constant which does not depend on $\theta$ and $q$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dasgupta:2007:CEU, author = "Samit Dasgupta", title = "Computations of Elliptic Units for Real Quadratic Fields", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "553--574", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-023-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a real quadratic field, and $p$ a rational prime which is inert in $K$. Let $\alpha$ be a modular unit on $\Gamma$_0$ (N)$. In an earlier joint article with Henri Darmon, we presented the definition of an element $u(\alpha, tau) \in K$_p^{times}$$ attached to $\alpha$ and each $tau \in K$. We conjectured that the $p$-adic number $u(\alpha, tau)$ lies in a specific ring class extension of $K$ depending on $tau$, and proposed a {``Shimura reciprocity law''} describing the permutation action of Galois on the set of $u(\alpha, tau)$. This article provides computational evidence for these conjectures. We present an efficient algorithm for computing $u(\alpha, tau)$, and implement this algorithm with the modular unit $\alpha(z) = \Delta(z)$^2$ \Delta(4z)/\Delta(2z)$^3$$. Using $p = 3, 5, 7,$ and $11$, and all real quadratic fields $K$ with discriminant $D < 500$ such that 2 splits in $K$ and $K$ contains no unit of negative norm, we obtain results supporting our conjectures. One of the theoretical results in this paper is that a certain measure used to define $u(\alpha, tau)$ is shown to be $(mathbf Z)$-valued rather than only $(mathbf Z)$_p$ \cap (mathbf Q)$-valued; this is an improvement over our previous result and allows for a precise definition of $u(\alpha, tau)$, instead of only up to a root of unity.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hernandez-Hernandez:2007:CIA, author = "Fernando Hern{\'a}ndez-Hern{\'a}ndez and Michael Hrus{\'a}k", title = "Cardinal Invariants of Analytic {$P$}-Ideals", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "575--595", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-024-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the cardinal invariants of analytic $P$-ideals, concentrating on the ideal $(\mathcal Z)$ of asymptotic density zero. Among other results we prove min ${(\mathfrak b), cov (\mathcal N)} \leq cov$^*$ (\mathcal Z) \leq $ max ${(\mathfrak b),$ non $(\mathcal N)}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Itza-Ortiz:2007:ETM, author = "Benjam{\'\i}n A. Itz{\'a}-Ortiz", title = "Eigenvalues, {$K$}-theory and Minimal Flows", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "596--613", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-025-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $(Y,T)$ be a minimal suspension flow built over a dynamical system $(X,S)$ and with (strictly positive, continuous) ceiling function $f : X \to (\mathbb R)$. We show that the eigenvalues of $(Y,T)$ are contained in the range of a trace on the $K$_0$$-group of $(X,S)$. Moreover, a trace gives an order isomorphism of a subgroup of $K$_0$ (\cprod{C(X)}{S})$ with the group of eigenvalues of $(Y,T)$. Using this result, we relate the values of $t$ for which the time- $t$ map on the minimal suspension flow is minimal with the $K$-theory of the base of this suspension.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Labuschagne:2007:PNO, author = "C. C. A. Labuschagne", title = "Preduals and Nuclear Operators Associated with Bounded, $p$-Convex, $p$-Concave and Positive $p$-Summing Operators", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "614--637", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-026-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of $p$-convex, $p$-concave and positive $p$-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{MacDonald:2007:DIN, author = "Gordon W. MacDonald", title = "Distance from Idempotents to Nilpotents", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "638--657", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-027-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give bounds on the distance from a non-zero idempotent to the set of nilpotents in the set of $n \times n$ matrices in terms of the norm of the idempotent. We construct explicit idempotents and nilpotents which achieve these distances, and determine exact distances in some special cases.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Minac:2007:DAP, author = "J. Min{\'a}c and A. Wadsworth", title = "Division Algebras of Prime Degree and Maximal {Galois} $p$-Extensions", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "658--672", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-028-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $p$ be an odd prime number, and let $F$ be a field of characteristic not $p$ and not containing the group $mu$_p$$ of $p$-th roots of unity. We consider cyclic $p$-algebras over $F$ by descent from $L = F(mu$_p$)$. We generalize a theorem of Albert by showing that if $mu$_{p$^n$}$ \subseteq L$, then a division algebra $D$ of degree $p$^n$$ over $F$ is a cyclic algebra if and only if there is $d \in D$ with d$^{p n}$ \in F - F^p. Let $F(p)$ be the maximal $p$-extension of $F$. We show that $F(p)$ has a noncyclic algebra of degree $p$ if and only if a certain eigencomponent of the $p$-torsion of Br $(F(p)(mu$_p$))$ is nontrivial. To get a better understanding of $F(p)$, we consider the valuations on $F(p)$ with residue characteristic not $p$, and determine what residue fields and value groups can occur. Our results support the conjecture that the $p$ torsion in Br $(F(p))$ is always trivial.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ash:2007:HFD, author = "Avner Ash and Solomon Friedberg", title = "{Hecke} {$L$}-Functions and the Distribution of Totally Positive Integers", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "673--695", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-029-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a totally real number field of degree $n$. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained from geometric considerations. This result depends on unfolding an integral over a compact torus.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bangoura:2007:ALH, author = "Momo Bangoura", title = "Alg{\`e}bres de {Lie} d'homotopie associ{\'e}es {\`a} une proto-big{\`e}bre de {Lie}", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "696--711", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-030-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "On associe {\`a} toute structure de proto-big{\`e}bre de Lie sur un espace vectoriel $F$ de dimension finie des structures d'alg{\`e}bre de Lie d'homotopie d{\'e}finies respectivement sur la suspension de l'alg{\`e}bre ext{\'e}rieure de $F$ et celle de son dual $F$^*$$. Dans ces alg{\`e}bres, tous les crochets $n$-aires sont nuls pour $n geq 4$ du fait qu'ils proviennent d'une structure de proto-big{\`e}bre de Lie. Plus g{\'e}n{\'e}ralement, on associe {\`a} un {\'e}l{\'e}ment de degr{\'e} impair de l'alg{\`e}bre ext{\'e}rieure de la somme directe de $F$ et $F$^*$$, une collection d'applications multilin{\'e}aires antisym{\'e}triques sur l'alg{\`e}bre ext{\'e}rieure de $F$ (resp. $F$^*$$), qui v{\'e}rifient les identit{\'e}s de Jacobi g{\'e}n{\'e}ralis{\'e}es, d{\'e}finissant les alg{\`e}bres de Lie d'homotopie, si l'{\'e}l{\'e}ment donn{\'e} est de carr{\'e} nul pour le grand crochet de l'alg{\`e}bre ext{\'e}rieure de la somme directe de $F$ et de $F$^*$$. To any proto-Lie algebra structure on a finite-dimensional vector space $F$, we associate homotopy Lie algebra structures defined on the suspension of the exterior algebra of $F$ and that of its dual $F$^*$$, respectively. In these algebras, all $n$-ary brackets for $n geq 4$ vanish because the brackets are defined by the proto-Lie algebra structure. More generally, to any element of odd degree in the exterior algebra of the direct sum of $F$ and $F$^*$$, we associate a set of multilinear skew-symmetric mappings on the suspension of the exterior algebra of $F$ (resp. $F$^*$$), which satisfy the generalized Jacobi identities, defining the homotopy Lie algebras, if the given element is of square zero with respect to the big bracket of the exterior algebra of the direct sum of $F$ and $F$^*$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Billig:2007:JM, author = "Yuly Billig", title = "Jet Modules", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "712--729", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-031-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we classify indecomposable modules for the Lie algebra of vector fields on a torus that admit a compatible action of the algebra of functions. An important family of such modules is given by spaces of jets of tensor fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Erdelyi:2007:LSI, author = "T. Erd{\'e}lyi and D. S. Lubinsky", title = "Large Sieve Inequalities via Subharmonic Methods and the {Mahler} Measure of the {Fekete} Polynomials", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "730--741", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-032-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate large sieve inequalities such as $frac{1}{m} sum$_{j=1}^m$ psi(log|P(e$^{i tau j}$)|) \leq frac{C}{2 pi} int$_0^{2 pi}$ psi(log[e|P(e$^{i tau}$)|])d tau,$ where $psi$ is convex and increasing, $P$ is a polynomial or an exponential of a potential, and the constant $C$ depends on the degree of $P$, and the distribution of the points $0 \leq tau$_1$ < tau$_2$ < ... < tau$_m$ \leq 2 pi$. The method allows greater generality and is in some ways simpler than earlier ones. We apply our results to estimate the Mahler measure of Fekete polynomials.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gil:2007:GSC, author = "Juan B. Gil and Thomas Krainer and Gerardo A. Mendoza", title = "Geometry and Spectra of Closed Extensions of Elliptic Cone Operators", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "742--794", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-033-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the geometry of the set of closed extensions of index 0 of an elliptic differential cone operator and its model operator in connection with the spectra of the extensions, and we give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jaworski:2007:CDE, author = "Wojciech Jaworski and Matthias Neufang", title = "The {Choquet--Deny} Equation in a {Banach} Space", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "795--827", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-034-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a locally compact group and $pi$ a representation of $G$ by weakly $$^*$$ continuous isometries acting in a dual Banach space $E$. Given a probability measure $mu$ on $G$, we study the Choquet--Deny equation $pi(mu)x = x$, $x \in E$. We prove that the solutions of this equation form the range of a projection of norm 1 and can be represented by means of a {``Poisson formula''} on the same boundary space that is used to represent the bounded harmonic functions of the random walk of law $mu$. The relation between the space of solutions of the Choquet--Deny equation in $E$ and the space of bounded harmonic functions can be understood in terms of a construction resembling the $W$^*$$-crossed product and coinciding precisely with the crossed product in the special case of the Choquet--Deny equation in the space $E = B(L$^2$ (G))$ of bounded linear operators on $L$^2$ (G)$. Other general properties of the Choquet--Deny equation in a Banach space are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ortner:2007:NBR, author = "Ronald Ortner and Wolfgang Woess", title = "Non-Backtracking Random Walks and Cogrowth of Graphs", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "828--844", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-035-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $X$ be a locally finite, connected graph without vertices of degree 1. Non-backtracking random walk moves at each step with equal probability to one of the {``forward''} neighbours of the actual state, $i.e.,$ it does not go back along the preceding edge to the preceding state. This is not a Markov chain, but can be turned into a Markov chain whose state space is the set of oriented edges of $X$. Thus we obtain for infinite $X$ that the $n$-step non-backtracking transition probabilities tend to zero, and we can also compute their limit when $X$ is finite. This provides a short proof of old results concerning cogrowth of groups, and makes the extension of that result to arbitrary regular graphs rigorous. Even when $X$ is non-regular, but $small cycles are dense in$ $X$, we show that the graph $X$ is non-amenable if and only if the non-backtracking $n$-step transition probabilities decay exponentially fast. This is a partial generalization of the cogrowth criterion for regular graphs which comprises the original cogrowth criterion for finitely generated groups of Grigorchuk and Cohen.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Schaffhauser:2007:RFG, author = "Florent Schaffhauser", title = "Representations of the Fundamental Group of an {$L$}-Punctured Sphere Generated by Products of {Lagrangian} Involutions", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "845--879", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-036-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we characterize unitary representations of $pi:= pi$_1$ (S$^2$ \backslash {s$_1$, dots, s$_1$})$ whose generators u$_1$, dots, u$_l$ (lying in conjugacy classes fixed initially) can be decomposed as products of two Lagrangian involutions $u$_j$ = \sigma$_j$ \sigma$_{j+1}$$ with $\sigma$_{l+1}$ = \sigma$_1$$. Our main result is that such representations are exactly the elements of the fixed-point set of an anti-symplectic involution defined on the moduli space ${mathcal M}$_e$:= Hom$_{{mathcal C}}$ (pi,U(n))/U(n)$. Consequently, as this fixed-point set is non-empty, it is a Lagrangian submanifold of ${mathcal M}$_e$$. To prove this, we use the quasi-Hamiltonian description of the symplectic structure of ${mathcal M}$_e$$ and give conditions on an involution defined on a quasi-Hamiltonian $U$-space $(M, \omega, mu: M \to U)$ for it to induce an anti-symplectic involution on the reduced space $M//U:= mu$^{-1}$ ({1})/U$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{denvan:2007:RIV, author = "John E. den van", title = "Radical Ideals in Valuation Domains", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "880--896", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-037-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "An ideal $I$ of a ring $R$ is called a radical ideal if $I = {mathcal R}(R)$ where ${mathcal R}$ is a radical in the sense of Kurosh--Amitsur. The main theorem of this paper asserts that if $R$ is a valuation domain, then a proper ideal $I$ of $R$ is a radical ideal if and only if $I$ is a distinguished ideal of $R$ (the latter property means that if $J$ and $K$ are ideals of $R$ such that $J subset I subset K$ then we cannot have $I/J cong K/I$ as rings) and that such an ideal is necessarily prime. Examples are exhibited which show that, unlike prime ideals, distinguished ideals are not characterizable in terms of a property of the underlying value group of the valuation domain.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bruneau:2007:GSP, author = "Laurent Bruneau", title = "The Ground State Problem for a Quantum {Hamiltonian} Model Describing Friction", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "897--916", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-038-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we consider the quantum version of a Hamiltonian model describing friction. This model consists of a particle which interacts with a bosonic reservoir representing a homogeneous medium through which the particle moves. We show that if the particle is confined, then the Hamiltonian admits a ground state if and only if a suitable infrared condition is satisfied. The latter is violated in the case of linear friction, but satisfied when the friction force is proportional to a higher power of the particle speed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Currey:2007:ACQ, author = "Bradley N. Currey", title = "Admissibility for a Class of Quasiregular Representations", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "917--942", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-039-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given a semidirect product $G = N rtimes H$ where $N$ is nilpotent, connected, simply connected and normal in $G$ and where $H$ is a vector group for which ad $(mathfrac h)$ is completely reducible and $mathbf R$-split, let $tau$ denote the quasiregular representation of $G$ in $L$^2$ (N)$. An element $psi \in L$^2$ (N)$ is said to be admissible if the wavelet transform $f mapsto langle f, tau (cdot) psi rangle$ defines an isometry from $L$^2$ (N)$ into $L$^2$ (G)$. In this paper we give an explicit construction of admissible vectors in the case where $G$ is not unimodular and the stabilizers in $H$ of its action on $hat N$ are almost everywhere trivial. In this situation we prove orthogonality relations and we construct an explicit decomposition of $L$^2$ (G)$ into $G$-invariant, multiplicity-free subspaces each of which is the image of a wavelet transform . We also show that, with the assumption of (almost-everywhere) trivial stabilizers, non-unimodularity is necessary for the existence of admissible vectors.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Finster:2007:WEW, author = "Felix Finster and Margarita Kraus", title = "A Weighted {$L^2$}-Estimate of the {Witten} Spinor in Asymptotically {Schwarzschild} Manifolds", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "943--965", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-040-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We derive a weighted $L$^2$$-estimate of the Witten spinor in a complete Riemannian spin manifold $(M$^n$, g)$ of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of $M$ enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of $M$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Forrest:2007:OAF, author = "Brian E. Forrest and Volker Runde and Nico Spronk", title = "Operator Amenability of the {Fourier} Algebra in the $\cb$-Multiplier Norm", journal = j-CAN-J-MATH, volume = "59", number = "5", pages = "966--980", month = oct, year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-041-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $G$ be a locally compact group, and let $A$_{cb}$ (G)$ denote the closure of $A(G)$, the Fourier algebra of $G$, in the space of completely bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group such that $cstar(G)$ is residually finite-dimensional, we show that $A$_{cb}$ (G)$ is operator amenable. In particular, $A$_{cb}$ (F$_2$)$ is operator amenable even though $F$_2$$, the free group in two generators, is not an amenable group. Moreover, we show that if $G$ is a discrete group such that $A$_{cb}$ (G)$ is operator amenable, a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$ if and only if it has an approximate identity bounded in the cb-multiplier norm.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jiang:2007:CRC, author = "Yunfeng Jiang", title = "The {Chen--Ruan} Cohomology of Weighted Projective Spaces", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "981--1007", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-042-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we study the Chen--Ruan cohomology ring of weighted projective spaces. Given a weighted projective space {\bf P}$^n_{q 0}$, \dots, q$_n$, we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen--Ruan cohomology ring of weighted projective space {\bf P}$^5_{1,2,2,3,3,3}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kaczynski:2007:IZT, author = "Tomasz Kaczynski and Marian Mrozek and Anik Trahan", title = "Ideas from {Zariski} Topology in the Study of Cubical Homology", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1008--1028", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-043-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Cubical sets and their homology have been used in dynamical systems as well as in digital imaging. We take a fresh look at this topic, following Zariski ideas from algebraic geometry. The cubical topology is defined to be a topology in $\mathbb R$^d$$ in which a set is closed if and only if it is cubical. This concept is a convenient frame for describing a variety of important features of cubical sets. Separation axioms which, in general, are not satisfied here, characterize exactly those pairs of points which we want to distinguish. The noetherian property guarantees the correctness of the algorithms. Moreover, maps between cubical sets which are continuous and closed with respect to the cubical topology are precisely those for whom the homology map can be defined and computed without grid subdivisions. A combinatorial version of the Vietoris-Begle theorem is derived. This theorem plays the central role in an algorithm computing homology of maps which are continuous with respect to the Euclidean topology.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kalton:2007:G, author = "N. J. Kalton and A. Koldobsky and V. Yaskin and M. Yaskina", title = "The Geometry of {$L_0$}", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1029--1068", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-044-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Suppose that we have the unit Euclidean ball in $\mathbb R$^n$$ and construct new bodies using three operations --- linear transformations, closure in the radial metric, and multiplicative summation defined by |x|$_{K+ 0}$ L = \sqrt{|x|$_K$ |x|$_L$}. We prove that in dimension 3 this procedure gives all origin-symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of a normed space in $L$_0$$ that naturally extends the corresponding properties of $L$_p$$-spaces with $p \ne 0$, and show that the procedure described above gives exactly the unit balls of subspaces of $L$_0$$ in every dimension. We provide Fourier analytic and geometric characterizations of spaces embedding in $L$_0$$, and prove several facts confirming the place of $L$_0$$ in the scale of $L$_p$$-spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Reydy:2007:QJA, author = "Carine Reydy", title = "Quotients jacobiens: une approche alg{\'e}brique. ({French}) [{Jacobian} quotients: an algebraic approach]", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1069--1097", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-046-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Le diagramme d'Eisenbud et Neumann d'un germe est un arbre qui repr{\'e}sente ce germe et permet d'en calculer les invariants. On donne une d{\'e}monstration alg{\'e}brique d'un r{\'e}sultat caract{\'e}risant l'ensemble des quotients jacobiens d'un germe d'application $(f,g)$ {\`a} partir du diagramme d'Eisenbud et Neumann de $fg$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Rodrigues:2007:RES, author = "B. Rodrigues", title = "Ruled Exceptional Surfaces and the Poles of {Motivic} Zeta Functions", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1098--1120", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-047-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper we study ruled surfaces which appear as an exceptional surface in a succession of blowing-ups. In particular we prove that the $e$-invariant of such a ruled exceptional surface $E$ is strictly positive whenever its intersection with the other exceptional surfaces does not contain a fiber (of $E$). This fact immediately enables us to resolve an open problem concerning an intersection configuration on such a ruled exceptional surface consisting of three nonintersecting sections. In the second part of the paper we apply the non-vanishing of $e$ to the study of the poles of the well-known topological, Hodge and motivic zeta functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Alayont:2007:MCS, author = "Fery{\^a}l Alayont", title = "Meromorphic Continuation of Spherical Cuspidal Data {Eisenstein} Series", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1121--1134", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-048-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Meromorphic continuation of the Eisenstein series induced from spherical, cuspidal data on parabolic subgroups is achieved via reworking Bernstein's adaptation of Selberg's third proof of meromorphic continuation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bjorn:2007:SEH, author = "Anders Bj{\"o}rn and Jana Bj{\"o}rn and Nageswari Shanmugalingam", title = "{Sobolev} Extensions of {H{\"o}lder} Continuous and Characteristic Functions on Metric Spaces", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1135--1153", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-049-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study when characteristic and H{\"o}lder continuous functions are traces of Sobolev functions on doubling metric measure spaces. We provide analytic and geometric conditions sufficient for extending characteristic and H{\"o}lder continuous functions into globally defined Sobolev functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Boardman:2007:TFS, author = "J. Michael Boardman and W. Stephen Wilson", title = "$k(n)$-Torsion-Free {$H$}-Spaces and {$P(n)$}-Cohomology", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1154--1206", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-050-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The $H$-space that represents Brown--Peterson cohomology BP $$^k$ (-)$ was split by the second author into indecomposable factors, which all have torsion-free homotopy and homology. Here, we do the same for the related spectrum $P(n)$, by constructing idempotent operations in $P(n)$-cohomology $P(n)$^k$ (--)$ in the style of Boardman--Johnson--Wilson; this relies heavily on the Ravenel--Wilson determination of the relevant Hopf ring. The resulting $(i - 1)$-connected $H$-spaces $Y$_i$$ have free connective Morava $K$-homology $k(n)$_*$ (Y$_i$)$, and may be built from the spaces in the $\Omega$-spectrum for $k(n)$ using only $v$_n$$-torsion invariants. We also extend Quillen's theorem on complex cobordism to show that for any space $X$, the $P(n)$_*$$-module $P(n)$^*$ (X)$ is generated by elements of $P(n)$^i$ (X)$ for $i \ge 0$. This result is essential for the work of Ravenel--Wilson--Yagita, which in many cases allows one to compute BP-cohomology from Morava $K$-theory.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bu:2007:MRO, author = "Shangquan Bu and Christian Merdy Le", title = "{$H^p$}-Maximal Regularity and Operator Valued Multipliers on {Hardy} Spaces", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1207--1222", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-051-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider maximal regularity in the $H^p$ sense for the Cauchy problem $u$^'$ (t) + Au(t) = f(t) (t \in {\mathbb R})$, where $A$ is a closed operator on a Banach space $X$ and $f$ is an $X$-valued function defined on ${\mathbb R}$. We prove that if $X$ is an AUMD Banach space, then $A$ satisfies $H^p$-maximal regularity if and only if $A$ is Rademacher sectorial of type $< \frac{\pi}{2}$. Moreover we find an operator $A$ with $H^p$-maximal regularity that does not have the classical $L^p$-maximal regularity. We prove a related Mikhlin type theorem for operator valued Fourier multipliers on Hardy spaces $H^p ({\mathbb R};X)$, in the case when $X$ is an AUMD Banach space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Buraczewski:2007:CZO, author = "Dariusz Buraczewski and Teresa Martinez and Jos{\'e} L. Torrea", title = "{Calder{\'o}n--Zygmund} Operators Associated to Ultraspherical Expansions", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1223--1244", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-052-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We define the higher order Riesz transforms and the Littlewood--Paley $g$-function associated to the differential operator $L$_\lambda$ f(\theta) = -f ``(\theta) - 2 \lambda cot \theta f$^'$ (\theta) + lambda$^2$ f (\theta)$''. We prove that these operators are Calder{\'o}n--Zygmund operators in the homogeneous type space $((0,pi),(sin t)$^{2 lambda}$ dt)$. Consequently, $L^p$ weighted, $H$^1$-L$^1$$ and $L$^\infty$- BMO$ inequalities are obtained.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2007:GPI, author = "Qun Chen and Zhen-Rong Zhou", title = "On Gap Properties and Instabilities of $p$-{Yang--Mills} Fields", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1245--1259", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-053-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider the $p$-Yang--Mills functional $(p \geq 2)$ defined as $YM$_p$ (nabla) := \frac 1 p \int$_M$ ||R$^{nabla}$ ||^p$. We call critical points of $YM$_p$ (cdot)$ the $p$-Yang--Mills connections, and the associated curvature $R$^{nabla}$$ the $p$-Yang--Mills fields. In this paper, we prove gap properties and instability theorems for $p$-Yang--Mills fields over submanifolds in $\mathbb{R}$^{n+k}$$ and $\mathbb{S}$^{n+k}$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Deng:2007:GEC, author = "Bangming Deng and Jie Du and Jie Xiao", title = "Generic Extensions and Canonical Bases for Cyclic Quivers", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1260--1283", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-054-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We use the monomial basis theory developed by Deng and Du to present an elementary algebraic construction of the canonical bases for both the Ringel--Hall algebra of a cyclic quiver and the positive part {\bf U}$^+$ of the quantum affine $frak{sl}$_n$$. This construction relies on analysis of quiver representations and the introduction of a new integral PBW-like basis for the Lusztig \mathbb Z[v,v$^{-1}$ ]-form of {\bf U}$^+$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fukshansky:2007:EWD, author = "Lenny Fukshansky", title = "On Effective {Witt} Decomposition and the {Cartan--Dieudonn{\'e}} Theorem", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1284--1300", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-055-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $K$ be a number field, and let $F$ be a symmetric bilinear form in $2N$ variables over $K$. Let $Z$ be a subspace of $K$^N$$. A classical theorem of Witt states that the bilinear space $(Z,F)$ can be decomposed into an orthogonal sum of hyperbolic planes and singular and anisotropic components. We prove the existence of such a decomposition of small height, where all bounds on height are explicit in terms of heights of $F$ and $Z$. We also prove a special version of Siegel's lemma for a bilinear space, which provides a small-height orthogonal decomposition into one-dimensional subspaces. Finally, we prove an effective version of the Cartan--Dieudonn{\'e} theorem. Namely, we show that every isometry $\sigma$ of a regular bilinear space $(Z,F)$ can be represented as a product of reflections of bounded heights with an explicit bound on heights in terms of heights of $F$, $Z$, and $\sigma$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Furioli:2007:SIW, author = "Giulia Furioli and Camillo Melzi and Alessandro Veneruso", title = "{Strichartz} Inequalities for the Wave Equation with the Full {Laplacian} on the {Heisenberg} Group", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1301--1322", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-056-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove dispersive and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on the Heisenberg group, by means of Besov spaces defined by a Littlewood--Paley decomposition related to the spectral resolution of the full Laplacian. This requires a careful analysis due also to the non-homogeneous nature of the full Laplacian. This result has to be compared to a previous one by Bahouri, G{\'e}rard and Xu concerning the solution of the wave equation related to the Kohn Laplacian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ginzburg:2007:CJL, author = "David Ginzburg and Erez Lapid", title = "On a Conjecture of {Jacquet}, {Lai}, and {Rallis}: Some Exceptional Cases", journal = j-CAN-J-MATH, volume = "59", number = "??", pages = "1323--1340", month = "????", year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-057-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove two spectral identities. The first one relates the relative trace formula for the spherical variety ${\rm GSpin}(4,3)/G_2$ with a weighted trace formula for $\GL_2$. The second relates a spherical variety pertaining to $F_4$ to one of ${\rm GSp}(6)$. These identities are in accordance with a conjecture made by Jacquet, Lai, and Rallis, and are obtained without an appeal to a geometric comparison.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anonymous:2007:AII, author = "Anonymous", title = "Author Index --- Index des auteurs --- for 2007 --- pour 2007", journal = j-CAN-J-MATH, volume = "59", number = "6", pages = "1341--1344", month = dec, year = "2007", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2007-058-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v59/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Boroczky:2008:CBM, author = "K{\'a}roly B{\"o}r{\"o}czky and K{\'a}roly J. B{\"o}r{\"o}czky and Carsten Sch{\"u}tt and Gergely Wintsche", title = "Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "3--32", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-001-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Given $r > 1$, we consider convex bodies in $E$^n$$ which contain a fixed unit ball, and whose extreme points are of distance at least $r$ from the centre of the unit ball, and we investigate how well these convex bodies approximate the unit ball in terms of volume, surface area and mean width. As $r$ tends to one, we prove asymptotic formulae for the error of the approximation, and provide good estimates on the involved constants depending on the dimension.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Braun:2008:HOT, author = "R{\"u}diger W. Braun and Reinhold Meise and B. A. Taylor", title = "Higher Order Tangents to Analytic Varieties along Curves. {II}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "33--63", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-002-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $V$ be an analytic variety in some open set in ${\mathbb C}$^n$$. For a real analytic curve $\gamma$ with $\gamma(0) = 0$ and $d \ge 1$ define $V$_t$ = t$^{-d}$ (V - \gamma(t))$. It was shown in a previous paper that the currents of integration over $V$_t$$ converge to a limit current whose support $T$_{\gamma,d}$ V$ is an algebraic variety as $t$ tends to zero. Here, it is shown that the canonical defining function of the limit current is the suitably normalized limit of the canonical defining functions of the $V$_t$$. As a corollary, it is shown that $T$_{\gamma,d}$ V$ is either inhomogeneous or coincides with $T$_{\gamma, \delta}$ V$ for all $\delta$ in some neighborhood of $d$. As another application it is shown that for surfaces only a finite number of curves lead to limit varieties that are interesting for the investigation of Phragm{\'e}n--Lindel{\"o}f conditions. Corresponding results for limit varieties $T$_{\sigma, \delta}$ W$ of algebraic varieties W along real analytic curves tending to infinity are derived by a reduction to the local case.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Daigle:2008:CLW, author = "Daniel Daigle", title = "Classification of Linear Weighted Graphs Up to Blowing-Up and Blowing-Down", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "64--87", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-003-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We classify linear weighted graphs up to the blowing-up and blowing-down operations which are relevant for the study of algebraic surfaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Diwadkar:2008:NCC, author = "Jyotsna Mainkar Diwadkar", title = "Nilpotent Conjugacy Classes in $p$-adic {Lie} Algebras: The Odd Orthogonal Case", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "88--108", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-004-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We will study the following question: Are nilpotent conjugacy classes of reductive Lie algebras over $p$-adic fields definable? By definable, we mean definable by a formula in Pas's language. In this language, there are no field extensions and no uniformisers. Using Waldspurger's parametrization, we answer in the affirmative in the case of special orthogonal Lie algebras $\mathfrak{so}(n)$ for $n$ odd, over $p$-adic fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gurjar:2008:ALA, author = "R. V. Gurjar and K. Masuda and M. Miyanishi and P. Russell", title = "Affine Lines on Affine Surfaces and the {Makar--Limanov} Invariant", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "109--139", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-005-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A smooth affine surface $X$ defined over the complex field ${\mathbb C}$ is an ML $$_0$$ surface if the Makar--Limanov invariant ML $(X)$ is trivial. In this paper we study the topology and geometry of ML $$_0$$ surfaces. Of particular interest is the question: Is every curve $C$ in $X$ which is isomorphic to the affine line a fiber component of an ${\mathbb A}$^1$$-fibration on $X$? We shall show that the answer is affirmative if the Picard number $rho(X) = 0$, but negative in case $rho(X) \ge 1$. We shall also study the ascent and descent of the ML $$_0$$ property under proper maps.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kedlaya:2008:GTC, author = "Kiran S. Kedlaya", title = "On the Geometry of $p$-Typical Covers in Characteristic $p$", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "140--163", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-006-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For $p$ a prime, a $p$-typical cover of a connected scheme on which $p = 0$ is a finite {\'e}tale cover whose monodromy group ( $i.e.,$ the Galois group of its normal closure) is a $p$-group. The geometry of such covers exhibits some unexpectedly pleasant behaviors; building on work of Katz, we demonstrate some of these. These include a criterion for when a morphism induces an isomorphism of the $p$-typical quotients of the {\'e}tale fundamental groups, and a decomposition theorem for $p$-typical covers of polynomial rings over an algebraically closed field.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2008:BSH, author = "Sangyop Lee and Masakazu Teragaito", title = "Boundary Structure of Hyperbolic $3$-Manifolds Admitting Annular and Toroidal Fillings at Large Distance", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "164--188", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-007-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a hyperbolic 3-manifold $M$ with a torus boundary component, all but finitely many Dehn fillings yield hyperbolic 3-manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such a situation, Gordon gave an upper bound of 5 for the distance between such slopes. Furthermore, the distance 4 is realized only by two specific manifolds, and 5 is realized by a single manifold. These manifolds all have a union of two tori as their boundaries. Also, there is a manifold with three tori as its boundary which realizes the distance 3. We show that if the distance is 3 then the boundary of the manifold consists of at most three tori.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lin:2008:FTA, author = "Huaxin Lin", title = "{Furstenberg} Transformations and Approximate Conjugacy", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "189--207", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-008-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $\alpha$ and $\beta$ be two Furstenberg transformations on 2-torus associated with irrational numbers $\theta$_1$$, $\theta$_2$$, integers $d$_1$, d$_2$$ and Lipschitz functions $f$_1$$ and $f$_2$$. It is shown that $\alpha$ and $\beta$ are approximately conjugate in a measure theoretical sense if (and only if) $\overline {\theta$_1$ \pm \theta$_2$}= 0$ in ${\mathbb R}/{\mathbb Z}$. Closely related to the classification of simple amenable $C$^*$$-algebras, it is shown that $\alpha$ and $\beta$ are approximately $K$-conjugate if (and only if) $\overline {\theta$_1$ \pm \theta$_2$} = 0$ in ${\mathbb R}/{\mathbb Z}$ and $|d$_1$ | = |d$_2$ |$. This is also shown to be equivalent to the condition that the associated crossed product $C$^*$$-algebras are isomorphic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ramakrishna:2008:CGR, author = "Ravi Ramakrishna", title = "Constructing {Galois} Representations with Very Large Image", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "208--221", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-009-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Starting with a 2-dimensional mod $p$ Galois representation, we construct a deformation to a power series ring in infinitely many variables over the $p$-adics. The image of this representation is full in the sense that it contains $SL$_2$$ of this power series ring. Furthermore, all ${\mathbb Z}$_p$$ specializations of this deformation are potentially semistable at $p$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Silipo:2008:ASE, author = "James Silipo", title = "Amibes de sommes d'exponentielles", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "222--240", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-010-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "L'objectif de cet article est d'{\'e}tudier la notion d'amibe au sens de Favorov pour les syst{\`e}mes finis de sommes d'exponentielles {\`a} fr{\'e}quences r{\'e}elles et de montrer que, sous des hypoth{\`e}ses de g{\'e}n{\'e}ricit{\'e} sur les fr{\'e}quences, le compl{\'e}mentaire de l'amibe d'un syst{\`e}me de $(k+1)$ sommes d'exponentielles {\`a} fr{\'e}quences r{\'e}elles est un sous-ensemble $k$-convexe au sens d'Henriques.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Alexandrova:2008:SCW, author = "Ivana Alexandrova", title = "Semi-Classical Wavefront Set and {Fourier} Integral Operators", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "241--263", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-011-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Here we define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators and prove a generalization of Egorov's theorem to manifolds of different dimensions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baake:2008:EES, author = "Michael Baake and Ellen Baake", title = "Erratum to: {``An Exactly Solved Model for Recombination, Mutation and Selection''}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "264--265", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-012-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{Baake:2003:ESM}.", abstract = ".", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bergeron:2008:ICS, author = "Nantel Bergeron and Christophe Reutenauer and Mercedes Rosas and Mike Zabrocki", title = "Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "266--296", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-013-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions. The bases for this algebra are indexed by set partitions. We show that there exists a natural inclusion of the Hopf algebra of noncommutative symmetric functions in this larger space. We also consider this algebra as a subspace of noncommutative polynomials and use it to understand the structure of the spaces of harmonics and coinvariants with respect to this collection of noncommutative polynomials and conclude two analogues of Chevalley's theorem in the noncommutative setting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bini:2008:TFH, author = "G. Bini and I. P. Goulden and D. M. Jackson", title = "Transitive Factorizations in the Hyperoctahedral Group", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "297--312", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-014-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The classical Hurwitz enumeration problem has a presentation in terms of transitive factorizations in the symmetric group. This presentation suggests a generalization from type $A$ to other finite reflection groups and, in particular, to type $B$. We study this generalization both from a combinatorial and a geometric point of view, with the prospect of providing a means of understanding more of the structure of the moduli spaces of maps with an $\mathfrak S$_2$$-symmetry. The type $A$ case has been well studied and connects Hurwitz numbers to the moduli space of curves. We conjecture an analogous setting for the type $B$ case that is studied here.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Choi:2008:API, author = "Yong-Kab Choi and Mikl{\'o}s Cs{\"o}rg\H o", title = "Asymptotic Properties for Increments of $l^{\infty}$-Valued {Gaussian} Random Fields", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "313--333", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-015-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper establishes general theorems which contain both moduli of continuity and large incremental results for $l$^\infty$$-valued Gaussian random fields indexed by a multidimensional parameter under explicit conditions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Curry:2008:LPF, author = "Eva Curry", title = "Low-Pass Filters and Scaling Functions for Multivariable Wavelets", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "334--347", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-016-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We show that a characterization of scaling functions for multiresolution analyses given by Hern{\'a}ndez and Weiss and that a characterization of low-pass filters given by Gundy both hold for multivariable multiresolution analyses.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Santos:2008:MFA, author = "F. Guill{\'e}n Santos and V. Navarro and P. Pascual and Agust{\'\i} Roig", title = "Monoidal Functors, Acyclic Models and Chain Operads", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "348--378", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-017-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C$_*^{ord}$ (P)$, and the operad of simplicial singular chains, $S$_*$ (P)$, are weakly equivalent. As a consequence, $C$_*^{ord}$ (P; \mathbb{Q})$ is formal if and only if $S$_*$ (P; \mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jorgensen:2008:FCM, author = "Peter J{\o}rgensen", title = "Finite {Cohen--Macaulay} Type and Smooth Non-Commutative Schemes", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "379--390", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-018-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "A commutative local Cohen--Macaulay ring $R$ of finite Cohen--Macaulay type is known to be an isolated singularity; that is, Spec $(R) setminus {\mathfrak {m}$ is smooth. This paper proves a non-commutative analogue. Namely, if $A$ is a (non-commutative) graded Artin--Schelter Cohen--Macaulay algebra which is fully bounded Noetherian and has finite Cohen--Macaulay type, then the non-commutative projective scheme determined by $A$ is smooth.??}", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Migliore:2008:GWL, author = "Juan C. Migliore", title = "The Geometry of the Weak {Lefschetz} Property and Level Sets of Points", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "391--411", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-019-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In a recent paper, F. Zanello showed that level Artinian algebras in 3 variables can fail to have the Weak Lefschetz Property (WLP), and can even fail to have unimodal Hilbert function. We show that the same is true for the Artinian reduction of reduced, level sets of points in projective 3-space. Our main goal is to begin an understanding of how the geometry of a set of points can prevent its Artinian reduction from having WLP, which in itself is a very algebraic notion. More precisely, we produce level sets of points whose Artinian reductions have socle types 3 and 4 and arbitrary socle degree $geq 12$ (in the worst case), but fail to have WLP. We also produce a level set of points whose Artinian reduction fails to have unimodal Hilbert function; our example is based on Zanello's example. Finally, we show that a level set of points can have Artinian reduction that has WLP but fails to have the Strong Lefschetz Property. While our constructions are all based on basic double G-linkage, the implementations use very different methods.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nguyen-Chu:2008:QCT, author = "G.-V. Nguyen-Chu", title = "Quelques calculs de traces compactes et leurs transform{\'e}es de {Satake}. ({French}) [{Some} calculations of compact traces and their {Satake} transforms]", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "412--442", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-020-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "On calcule les restrictions {\`a} l'alg{\`e}bre de Hecke sph{\'e}rique des traces tordues compactes d'un ensemble de repr{\'e}sentations explicitement construites du groupe {\bf GL} $(N, F)$, o{\`u} $F$ est un corps $p$-adique. Ces calculs r{\'e}solve en particulier une question pos{\'e}e dans un article pr{\'e}c{\'e}dent du m{\^e}me auteur.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Shen:2008:CPF, author = "Z. Shen and G. Civi Yildirim", title = "On a Class of Projectively Flat Metrics with Constant Flag Curvature", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "443--456", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-021-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In this paper, we find equations that characterize locally projectively flat Finsler metrics in the form $F = (\alpha + \beta)$^2$ /\alpha$, where $\alpha = \sqrt{a$_{ij}$ y$^i$ y$^j$}$ is a Riemannian metric and $\beta = b$_i$ y$^i$$ is a 1-form. Then we completely determine the local structure of those with constant flag curvature.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Teplyaev:2008:HCF, author = "Alexander Teplyaev", title = "Harmonic Coordinates on Fractals with Finitely Ramified Cell Structure", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "457--480", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-022-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We define sets with finitely ramified cell structure, which are generalizations of post-critically finite self-similar sets introduced by Kigami and of fractafolds introduced by Strichartz. In general, we do not assume even local self-similarity, and allow countably many cells connected at each junction point. In particular, we consider post-critically infinite fractals. We prove that if Kigami's resistance form satisfies certain assumptions, then there exists a weak Riemannian metric such that the energy can be expressed as the integral of the norm squared of a weak gradient with respect to an energy measure. Furthermore, we prove that if such a set can be homeomorphically represented in harmonic coordinates, then for smooth functions the weak gradient can be replaced by the usual gradient. We also prove a simple formula for the energy measure Laplacian in harmonic coordinates.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Breuer:2008:HPR, author = "Florian Breuer and Bo-Hae Im", title = "{Heegner} Points and the Rank of Elliptic Curves over Large Extensions of Global Fields", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "481--490", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-023-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $k$ be a global field, $\overline {k}$ a separable closure of $k$, and $G$_k$$ the absolute Galois group $Gal(\overline {k}/k)$ of $\overline {k}$ over $k$. For every $\sigma \in G$_k$$, let $\overline {k}$^{\sigma}$$ be the fixed subfield of $\overline {k}$ under $\sigma$. Let $E/k$ be an elliptic curve over $k$. It is known that the Mordell--Weil group $E(\overline {k}$^{\sigma}$)$ has infinite rank. We present a new proof of this fact in the following two cases. First, when $k$ is a global function field of odd characteristic and $E$ is parametrized by a Drinfeld modular curve, and secondly when $k$ is a totally real number field and $E/k$ is parametrized by a Shimura curve. In both cases our approach uses the non-triviality of a sequence of Heegner points on $E$ defined over ring class fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bugeaud:2008:MFA, author = "Yann Bugeaud and Maurice Mignotte and Samir Siksek", title = "A Multi-{Frey} Approach to Some Multi-Parameter Families of {Diophantine} Equations", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "491--519", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-024-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation 5$^u$ x$^n$-2$^r$ 3$^s$ y$^n$ = \pm 1, in non-zero integers $x$, $y$ and positive integers $u$, $r$, $s$ and $n \geq 3$. Our approach uses several Frey curves simultaneously, Galois representations and level-lowering, new lower bounds for linear forms in 3 logarithms due to Mignotte and a famous theorem of Bennett on binomial Thue equations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2008:MWN, author = "Chang-Pao Chen and Hao-Wei Huang and Chun-Yen Shen", title = "Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "520--531", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-025-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $A = (a$_{j,k}$)$_{j,k \ge 1}$$ be a non-negative matrix. In this paper, we characterize those $A$ for which $||A||$_{E, F}$$ are determined by their actions on decreasing sequences, where $E$ and $F$ are suitable normed Riesz spaces of sequences. In particular, our results can apply to the following spaces: $ell$_p$$, $d(w,p)$, and $ell$_p$ (w)$. The results established here generalize ones given by Bennett; Chen, Luor, and Ou; Jameson; and Jameson and Lashkaripour.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Clark:2008:LBT, author = "Pete L. Clark and Xavier Xarles", title = "Local Bounds for Torsion Points on {Abelian} Varieties", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "532--555", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-026-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We say that an abelian variety over a $p$-adic field $K$ has anisotropic reduction (AR) if the special fiber of its N{\'e}ron minimal model does not contain a nontrivial split torus. This includes all abelian varieties with potentially good reduction and, in particular, those with complex or quaternionic multiplication. We give a bound for the size of the $K$-rational torsion subgroup of a $g$-dimensional AR variety depending only on $g$ and the numerical invariants of $K$ (the absolute ramification index and the cardinality of the residue field). Applying these bounds to abelian varieties over a number field with everywhere locally anisotropic reduction, we get bounds which, as a function of $g$, are close to optimal. In particular, we determine the possible cardinalities of the torsion subgroup of an AR abelian surface over the rational numbers, up to a set of 11 values which are not known to occur. The largest such value is 72.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Draisma:2008:PSI, author = "Jan Draisma and Gregor Kemper and David Wehlau", title = "Polarization of Separating Invariants", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "556--571", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-027-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We prove a characteristic free version of Weyl's theorem on polarization. Our result is an exact analogue of Weyl's theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of $cheap polarization$, and show that it is enough to take cheap polarizations of invariants of just one copy of a representation to obtain separating vector invariants for any number of copies. This leads to upper bounds on the number and degrees of separating vector invariants of finite groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hitrik:2008:NSP, author = "Michael Hitrik and Johannes Sj{\"o}strand", title = "Non-Selfadjoint Perturbations of Selfadjoint Operators in Two Dimensions {IIIa}. One Branching Point", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "572--657", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-028-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, having a periodic classical flow. Assuming that the strength $epsilon$ of the perturbation is in the range $h$^2$ < < epsilon < < h$^{1/2}$$ (and may sometimes reach even smaller values), we get an asymptotic description of the eigenvalues in rectangles $[-1/C, 1/C] + i epsilon [F$_0$- 1/C, F$_0$ + 1/C]$, $C > > 1$, when $epsilon F$_0$$ is a saddle point value of the flow average of the leading perturbation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mihailescu:2008:IPE, author = "Eugen Mihailescu and Mariusz Urba{\'n}ski", title = "Inverse Pressure Estimates and the Independence of Stable Dimension for Non-Invertible Maps", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "658--684", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-029-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the case of an Axiom A holomorphic non-degenerate (hence non-invertible) map $f \from {\mathbb P}$^2$ {\mathbb C} \to {\mathbb P}$^2$ {\mathbb C}$, where ${\mathbb P}$^2$ {\mathbb C}$ stands for the complex projective space of dimension 2. Let $Lambda$ denote a basic set for $f$ of unstable index 1, and $x$ an arbitrary point of $Lambda$; we denote by $\delta$^s$ (x)$ the Hausdorff dimension of $W$^s_r$ (x) \cap Lambda$, where $r$ is some fixed positive number and $W$^s_r$ (x)$ is the local stable manifold at $x$ of size $r$; $\delta$^s$ (x)$ is called $the stable dimension at$ $x$. Mihailescu and Urbanski introduced a notion of inverse topological pressure, denoted by $P$^{-, which takes into consideration preimages of points. Manning and McCluskey study the case of hyperbolic diffeomorphisms on real surfaces and give formulas for Hausdorff dimension. Our non-invertible situation is different here since the local unstable manifolds are not uniquely determined by their base point, instead they depend in general on whole prehistories of the base points. Hence our methods are different and are based on using a sequence of inverse pressures for the iterates of f, in order to give upper and lower estimates of the stable dimension. We obtain an estimate of the oscillation of the stable dimension on Lambda. When each point x from Lambda has the same number d' of preimages in Lambda, then we show that \delta s}$ (x)$ is independent of $x$; in fact $\delta$^s$ (x)$ is shown to be equal in this case with the unique zero of the map $t \to P(t phi$^s$- log d')$. We also prove the Lipschitz continuity of the stable vector spaces over $Lambda$; this proof is again different than the one for diffeomorphisms (however, the unstable distribution is not always Lipschitz for conformal non-invertible maps). In the end we include the corresponding results for a real conformal setting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Savu:2008:CEF, author = "Anamaria Savu", title = "Closed and Exact Functions in the Context of {Ginzburg--Landau} Models", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "685--702", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-030-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "For a general vector field we exhibit two Hilbert spaces, namely the space of so called $closed functions$ and the space of $exact functions$ and we calculate the codimension of the space of exact functions inside the larger space of closed functions. In particular we provide a new approach for the known cases: the Glauber field and the second-order Ginzburg--Landau field and for the case of the fourth-order Ginzburg--Landau field.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Toms:2008:SAA, author = "Andrew S. Toms and Wilhelm Winter", title = "{$\mathcal{Z}$}-Stable {ASH} Algebras", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "703--733", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-031-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Jiang--Su algebra $mathcal Z$ has come to prominence in the classification program for nuclear $C$^*$$-algebras of late, due primarily to the fact that Elliott's classification conjecture in its strongest form predicts that all simple, separable, and nuclear $C$^*$$-algebras with unperforated $mathrm K$-theory will absorb $mathcal Z$ tensorially, $i.e.,$ will be $mathcal Z$-stable. There exist counterexamples which suggest that the conjecture will only hold for simple, nuclear, separable and $mathcal Z$-stable $C$^*$$-algebras. We prove that virtually all classes of nuclear $C$^*$$-algebras for which the Elliott conjecture has been confirmed so far consist of $mathcal Z$-stable $C$^*$$-algebras. This follows in large part from the following result, also proved herein: separable and approximately divisible $C$^*$$-algebras are $mathcal Z$-stable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baba:2008:GCQ, author = "Srinath Baba and H{\aa}kan Granath", title = "Genus 2 Curves with Quaternionic Multiplication", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "734--757", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-033-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We explicitly construct the canonical rational models of Shimura curves, both analytically in terms of modular forms and algebraically in terms of coefficients of genus 2 curves, in the cases of quaternion algebras of discriminant 6 and 10. This emulates the classical construction in the elliptic curve case. We also give families of genus 2 QM curves, whose Jacobians are the corresponding abelian surfaces on the Shimura curve, and with coefficients that are modular forms of weight 12. We apply these results to show that our $j$-functions are supported exactly at those primes where the genus 2 curve does not admit potentially good reduction, and construct fields where this potentially good reduction is attained. Finally, using $j$, we construct the fields of moduli and definition for some moduli problems associated to the Atkin--Lehner group actions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bercovici:2008:HSP, author = "H. Bercovici and C. Foias and C. Pearcy", title = "On the Hyperinvariant Subspace Problem. {IV}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "758--789", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-034-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper is a continuation of three recent articles concerning the structure of hyperinvariant subspace lattices of operators on a (separable, infinite dimensional) Hilbert space $H$. We show herein, in particular, that there exists a {``universal''} fixed block-diagonal operator $B$ on $H$ such that if {\epsilon} > 0 is given and $T$ is an arbitrary nonalgebraic operator on $H$, then there exists a compact operator $K$ of norm less than {\epsilon} such that (i) Hlat $(T)$ is isomorphic as a complete lattice to Hlat $(B + K)$ and (ii) $B + K$ is a quasidiagonal, $C$_{00}$$, (BCP)-operator with spectrum and left essential spectrum the unit disc. In the last four sections of the paper, we investigate the possible structures of the hyperlattice of an arbitrary algebraic operator. Contrary to existing conjectures, Hlat $(T)$ need not be generated by the ranges and kernels of the powers of $T$ in the nilpotent case. In fact, this lattice can be infinite.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Blasco:2008:TPC, author = "Laure Blasco", title = "Types, paquets et changement de base: l'exemple de {$U(2, 1)(F_0)$}. {I}. Types simples maximaux et paquets singletons. ({French}) [{Types}, packages and base change: the case of {$U(2, 1)(F_0)$}. {I}. {Simple} maximal types and singleton packets]", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "790--821", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-035-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Soit $F$_0$$ un corps local non archim{\'e}dien de caract{\'e}ristique nulle et de caract{\'e}ristique r{\'e}siduelle impaire. J. Rogawski a montr{\'e} l'existence du changement de base entre le groupe unitaire en trois variables $U(2,1)(F$_0$)$, d{\'e}fini relativement {\`a} une extension quadratique $F$ de $F$_0$$, et le groupe lin{\'e}aire GL $(3,F)$. Par ailleurs, nous avons d{\'e}crit les repr{\'e}sentations supercuspidales irr{\'e}ductibles de $U(2,1)(F$_0$)$ comme induites {\`a} partir d'un sous-groupe compact ouvert de $U(2,1)(F$_0$)$, description analogue {\`a} celle des repr{\'e}sentations admissibles irr{\'e}ductibles de GL $(3,F)$ obtenue par C. Bushnell et P. Kutzko. A partir de ces descriptions, nous construisons explicitement le changement de base des repr{\'e}sentations tr{\`e}s cuspidales de $U(2,1)(F$_0$)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Kuwae:2008:MPS, author = "Kazuhiro Kuwae", title = "Maximum Principles for Subharmonic Functions Via Local Semi-{Dirichlet} Forms", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "822--874", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-036-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Maximum principles for subharmonic functions in the framework of quasi-regular local semi-Dirichlet forms admitting lower bounds are presented. As applications, we give weak and strong maximum principles for (local) subsolutions of a second order elliptic differential operator on the domain of Euclidean space under conditions on coefficients, which partially generalize the results by Stampacchia.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mare:2008:CQC, author = "Augustin-Liviu Mare", title = "A Characterization of the Quantum Cohomology Ring of {$G / B$} and Applications", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "875--891", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-037-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We observe that the small quantum product of the generalized flag manifold $G/B$. is a product operation $star$ on $H$^*$ (G/B) \otimes {\mathbb R}[q$_1$, dots, q$_l$ ]$ uniquely determined by the facts that: it is a deformation of the cup product on $H$^*$ (G/B)$; it is commutative, associative, and graded with respect to deg $(q$_i$) = 4$; it satisfies a certain relation (of degree two); and the corresponding Dubrovin connection is flat. Previously, we proved that these properties alone imply the presentation of the ring $(H$^*$ (G/B) \otimes {\mathbb R}[q$_1$, dots, q$_l$ ], star)$ in terms of generators and relations. In this paper we use the above observations to give conceptually new proofs of other fundamental results of the quantum Schubert calculus for $G/B$: the quantum Chevalley formula of D. Peterson (see also Fulton and Woodward) and the {``quantization by standard monomials''} formula of Fomin, Gelfand, and Postnikov for $G = SL(n,{\mathbb C})$. The main idea of the proofs is the same as in Amarzaya--Guest: from the quantum {\cal D} -module of $G/B$ one can decode all information about the quantum cohomology of this space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Neeb:2008:SCC, author = "Karl-Hermann Neeb and Friedrich Wagemann", title = "The Second Cohomology of Current Algebras of General {Lie} Algebras", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "892--922", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-038-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $A$ be a unital commutative associative algebra over a field of characteristic zero, $\k$ a Lie algebra, and $\zf$ a vector space, considered as a trivial module of the Lie algebra $\gf := A \otimes \kf$. In this paper, we give a description of the cohomology space $H$^2$ (\gf, \zf)$ in terms of easily accessible data associated with $A$ and $\kf$ We also discuss the topological situation, where $A$ and $\kf$ are locally convex algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Okoh:2008:EKM, author = "F. Okoh and F. Zorzitto", title = "Endomorphisms of {Kronecker} Modules Regulated by Quadratic Algebra Extensions of a Function Field", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "923--957", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-039-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The Kronecker modules $\mathbb{V}(m,h, \alpha)$, where $m$ is a positive integer, $h$ is a height function, and $\alpha$ is a $K$-linear functional on the space $K(X)$ of rational functions in one variable $X$ over an algebraically closed field $K$, are models for the family of all torsion-free rank-2 modules that are extensions of finite-dimensional rank-1 modules. Every such module comes with a regulating polynomial $f$ in $K(X)[Y]$. When the endomorphism algebra of $\mathbb{V}(m,h, \alpha)$ is commutative and non-trivial, the regulator $f$ must be quadratic in $Y$. If $f$ has one repeated root in $K(X)$, the endomorphism algebra is the trivial extension $K ltimes S$ for some vector space $S$. If $f$ has distinct roots in $K(X)$, then the endomorphisms form a structure that we call a bridge. These include the coordinate rings of some curves. Regardless of the number of roots in the regulator, those End $\mathbb{V}(m,h, \alpha)$ that are domains have zero radical. In addition, each semi-local End $\mathbb{V}(m,h, \alpha)$ must be either a trivial extension $K ltimes S$ or the product $K times K$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2008:NCS, author = "Yichao Chen", title = "A Note on a Conjecture of {S. Stahl}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "958--959", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-040-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "S. Stahl (Canad. J. Math. {\bf 49} (1997), no. 3, 617--640) conjectured that the zeros of genus polynomial are real. L. Liu and Y. Wang disproved this conjecture on the basis of Example 6.7. In this note, it is pointed out that there is an error in this example and a new generating matrix and initial vector are provided.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Stahl:2008:EZS, author = "Saul Stahl", title = "Erratum: {``On the Zeros of Some Genus Polynomials''}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "960--960", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-041-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", note = "See \cite{Stahl:1997:ZSG}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Abrescia:2008:ADC, author = "Silvia Abrescia", title = "About the Defectivity of Certain {Segre--Veronese} Varieties", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "961--974", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-042-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We study the regularity of the higher secant varieties of $\mathbb P$^1$ times \mathbb P$^n$$, embedded with divisors of type $(d,2)$ and $(d,3)$. We produce, for the highest defective cases, a {``determinantal''} equation of the secant variety. As a corollary, we prove that the Veronese triple embedding of $\mathbb P$^n$$ is not Grassmann defective.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Boca:2008:AAA, author = "Florin P. Boca", title = "An {AF} Algebra Associated with the {Farey} Tessellation", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "975--1000", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-043-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We associate with the Farey tessellation of the upper half-plane an AF algebra $gothic U$ encoding the {``cutting sequences''} that define vertical geodesics. The Effros--Shen AF algebras arise as quotients of $gothic U$. Using the path algebra model for AF algebras we construct, for each $tau \in (0, 1/4]$, projections $(E$_n$)$ in $gothic U$ such that $E$_n$ E$_{n \pm 1}$ E$_n$ \leq tau E$_n$$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{deCornulier:2008:IGA, author = "Yves de Cornulier and Romain Tessera and Alain Valette", title = "Isometric Group Actions on {Hilbert} Spaces: Structure of Orbits", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1001--1009", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-044-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gale:2008:FCM, author = "Jos{\'e} E. Gal{\'e} and Pedro J. Miana", title = "{{$H^\infty$}} Functional Calculus and {Mikhlin}-Type Multiplier Conditions", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1010--1027", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-045-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $T$ be a sectorial operator. It is known that the existence of a bounded (suitably scaled) $H$^\infty$$ calculus for $T$, on every sector containing the positive half-line, is equivalent to the existence of a bounded functional calculus on the Besov algebra $Lambda$_{\infty,1}^{\alpha}$ (\mathbb R$^+$)$. Such an algebra includes functions defined by Mikhlin-type conditions and so the Besov calculus can be seen as a result on multipliers for $T$. In this paper, we use fractional derivation to analyse in detail the relationship between $Lambda$_{\infty,1}^{\alpha}$$ and Banach algebras of Mikhlin-type. As a result, we obtain a new version of the quoted equivalence.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hamblen:2008:LDG, author = "Spencer Hamblen", title = "Lifting $n$-Dimensional {Galois} Representations", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1028--1049", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-046-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We investigate the problem of deforming $n$-dimensional mod $p$ Galois representations to characteristic zero. The existence of 2-dimensional deformations has been proven under certain conditions by allowing ramification at additional primes in order to annihilate a dual Selmer group. We use the same general methods to prove the existence of $n$-dimensional deformations. We then examine under which conditions we may place restrictions on the shape of our deformations at $p$, with the goal of showing that under the correct conditions, the deformations may have locally geometric shape. We also use the existence of these deformations to prove the existence as Galois groups over $\mathbb Q$ of certain infinite subgroups of $p$-adic general linear groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Huang:2008:APM, author = "Wen-ling Huang and Peter \v Semrl", title = "Adjacency Preserving Maps on {Hermitian} Matrices", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1050--1066", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-047-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Hua's fundamental theorem of the geometry of hermitian matrices characterizes bijective maps on the space of all $n \times n$ hermitian matrices preserving adjacency in both directions. The problem of possible improvements has been open for a while. There are three natural problems here. Do we need the bijectivity assumption? Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only? Can we obtain such a characterization for maps acting between the spaces of hermitian matrices of different sizes? We answer all three questions for the complex hermitian matrices, thus obtaining the optimal structural result for adjacency preserving maps on hermitian matrices over the complex field.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kariyama:2008:TUA, author = "Kazutoshi Kariyama", title = "On Types for Unramified $p$-Adic Unitary Groups", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1067--1107", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-048-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Let $F$ be a non-archimedean local field of residue characteristic neither 2 nor 3 equipped with a galois involution with fixed field $F$_0$$, and let $G$ be a symplectic group over $F$ or an unramified unitary group over $F$_0$$. Following the methods of Bushnell--Kutzko for GL $(N,F)$, we define an analogue of a simple type attached to a certain skew simple stratum, and realize a type in $G$. In particular, we obtain an irreducible supercuspidal representation of $G$ like GL $(N,F)$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lopez-Abad:2008:CTT, author = "J. Lopez-Abad and A. Manoussakis", title = "A Classification of {Tsirelson} Type Spaces", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1108--1167", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-049-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We give a complete classification of mixed Tsirelson spaces $T[(\mathcal F_i, \theta_i)_{i = 1}^r]$ for finitely many pairs of given compact and hereditary families $\mathcal{F}_i$ of finite sets of integers and $0 < \theta_i < 1$ in terms of the Cantor--Bendixson indices of the families $\mathcal{F}_i$, and $\theta_i$ ($1 \le i \le r$). We prove that there are unique countable ordinal $\alpha$ and $0 < \theta < 1$ such that every block sequence of $T[(\mathcal F$_i$, \theta$_i$)$_{i=1}^r$ ]$ has a subsequence equivalent to a subsequence of the natural basis of the $T(\mathcal S_{\omega^{\alpha}}, \theta)$. Finally, we give a complete criterion of comparison in between two of these mixed Tsirelson spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Taylor:2008:STB, author = "Michael Taylor", title = "Short Time Behavior of Solutions to Linear and Nonlinear {Schr{\"o}dinger} Equations", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1168--1200", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-051-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We examine the fine structure of the short time behavior of solutions to various linear and nonlinear Schr{\"o}dinger equations $u$_t$ = i \Delta u + q(u)$ on $I \times {\mathbb R}$^n$$, with initial data $u(0,x) = f(x)$. Particular attention is paid to cases where $f$ is piecewise smooth, with jump across an $(n-1)$-dimensional surface. We give detailed analyses of Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon. We give results for general $n$ in the linear case. We also have detailed analyses for a broad class of nonlinear equations when $n = 1$ and 2, with emphasis on the analysis of the first order correction to the solution of the corresponding linear equation. This work complements estimates on the error in this approximation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bahuaud:2008:HCS, author = "Eric Bahuaud and Tracey Marsh", title = "{H{\"o}lder} Compactification for Some Manifolds with Pinched Negative Curvature Near Infinity", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1201--1218", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-051-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We consider a complete noncompact Riemannian manifold $M$ and give conditions on a compact submanifold $K \subset M$ so that the outward normal exponential map off the boundary of $K$ is a diffeomorphism onto $M\K$. We use this to compactify $M$ and show that pinched negative sectional curvature outside $K$ implies $M$ has a compactification with a well-defined H{\"o}lder structure independent of $K$. The H{\"o}lder constant depends on the ratio of the curvature pinching. This extends and generalizes a 1985 result of Anderson and Schoen.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baracco:2008:CEM, author = "Luca Baracco and Giuseppe Zampieri", title = "{CR} Extension from Manifolds of Higher Type", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1219--1239", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-052-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper deals with the extension of CR functions from a manifold $M \subset {\mathbb C}$^n$$ into directions produced by higher order commutators of holomorphic and antiholomorphic vector fields. It uses the theory of complex {``sectors''} attached to real submanifolds introduced in recent joint work of the authors with D. Zaitsev. In addition, it develops a new technique of approximation of sectors by smooth discs.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Beliakova:2008:CCJ, author = "Anna Beliakova and Stephan Wehrli", title = "Categorification of the Colored {Jones} Polynomial and {Rasmussen} Invariant of Links", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1240--1266", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-053-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples where this invariant is a stronger obstruction to sliceness than the multivariable Levine--Tristram signature.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Blake:2008:NRE, author = "Ian F. Blake and V. Kumar Murty and Guangwu Xu", title = "Nonadjacent {Radix-$\tau$} Expansions of Integers in {Euclidean} Imaginary Quadratic Number Fields", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1267--1282", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-054-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "In his seminal papers, Koblitz proposed curves for cryptographic use. For fast operations on these curves, these papers also initiated a study of the radix- $tau$ expansion of integers in the number fields ${\mathbb Q}(\sqrt{-3})$ and ${\mathbb Q}(\sqrt{-7})$. The (window) nonadjacent form of $tau$-expansion of integers in ${\mathbb Q}(\sqrt{-7})$ was first investigated by Solinas. For integers in ${\mathbb Q}(\sqrt{-3})$, the nonadjacent form and the window nonadjacent form of the $tau$-expansion were studied. These are used for efficient point multiplications on Koblitz curves. In this paper, we complete the picture by producing the (window) nonadjacent radix- $tau$ expansions for integers in all Euclidean imaginary quadratic number fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ho:2008:RLP, author = "Kwok-Pun Ho", title = "Remarks on {Littlewood--Paley} Analysis", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1283--1305", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-055-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Littlewood--Paley analysis is generalized in this article. We show that the compactness of the Fourier support imposed on the analyzing function can be removed. We also prove that the Littlewood--Paley decomposition of tempered distributions converges under a topology stronger than the weak-star topology, namely, the inductive limit topology. Finally, we construct a multiparameter Littlewood--Paley analysis and obtain the corresponding {``renormalization''} for the convergence of this multiparameter Littlewood--Paley analysis.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Muic:2008:TLT, author = "Goran Mui{\'c}", title = "Theta Lifts of Tempered Representations for Dual Pairs {$(\Sp_{2 n}, O(V))$}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1306--1335", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-056-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "This paper is the continuation of our previous work on the explicit determination of the structure of theta lifts for dual pairs $($ S {\bf p} $$_{2n}$, O(V))$ over a non-archimedean field $F$ of characteristic different than 2, where $n$ is the split rank of S {\bf p}$_{2n}$ and the dimension of the space $V$ (over $F$) is even. We determine the structure of theta lifts of tempered representations in terms of theta lifts of representations in discrete series.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Olver:2008:MFL, author = "Peter J. Olver and Juha Pohjanpelto", title = "Moving Frames for {Lie} {Pseudo--Groups}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1336--1386", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-057-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "We propose a new, constructive theory of moving frames for Lie pseudo-group actions on submanifolds. The moving frame provides an effective means for determining complete systems of differential invariants and invariant differential forms, classifying their syzygies and recurrence relations, and solving equivalence and symmetry problems arising in a broad range of applications.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Romo:2008:DSS, author = "Fernando Pablos Romo", title = "On $n$-Dimensional {Steinberg} Symbols", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1387--1405", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-058-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "The aim of this work is to provide a new approach for constructing $n$-dimensional Steinberg symbols on discrete valuation fields from $(n+1)$-cocycles and to study reciprocity laws on curves related to these symbols.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ricotta:2008:HAP, author = "Guillaume Ricotta and Thomas Vidick", title = "Hauteur asymptotique des points de {Heegner}", journal = j-CAN-J-MATH, volume = "60", number = "??", pages = "1406--1436", month = "????", year = "2008", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-2008-059-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:14 MDT 2011", bibsource = "http://cms.math.ca/cjm/v60/; http://www.math.utah.edu/pub/tex/bib/canjmath2000.bib", abstract = "Geometric intuition suggests that the N{\'e}ron--Tate height of Heegner points on a rational elliptic curve $E$ should be asymptotically governed by the degree of its modular parametrisation. In this paper, we show that this geometric intuition asymptotically holds on average over a subset of discriminants. We also study the asymptotic behaviour of traces of Heegner points on average over a subset of discriminants and find a difference according to the rank of the elliptic curve. By the Gross--Zagier formulae, such heights are related to the special value at the critical point for either the derivative of the Rankin--Selberg convolution of $E$ with a certain weight one theta series attached to the principal ideal class of an imaginary quadratic field or the twisted $L$-function of $E$ by a quadratic Dirichlet character. Asymptotic formulae for the first moments associated with these $L$-series and $L$-functions are proved, and experimental results are discussed. The