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Abstract of a paper by Mark Rudelson and Roman Vershynin
by Dale Alspach 21 Mar '07

21 Mar '07

This is an announcement for the paper "The Littlewood-Offord Problem and invertibility of random matrices" by Mark Rudelson and Roman Vershynin. Abstract: We prove two basic conjectures on the distribution of the smallest singular value of random n times n matrices with independent entries. Under minimal moment assumptions, we show that the smallest singular value is of order n^{-1/2}, which is optimal for Gaussian matrices. Moreover, we give a optimal estimate on the tail probability. This comes as a consequence of a new and essentially sharp estimate in the Littlewood-Offord problem: for i.i.d. random variables X_k and real numbers a_k, determine the probability P that the sum of a_k X_k lies near some number v. For arbitrary coefficients a_k of the same order of magnitude, we show that they essentially lie in an arithmetic progression of length 1/p. Archive classification: Probability; Functional Analysis Mathematics Subject Classification: 15A52; 11P70 Remarks: 35 pages, no figures Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.PR/0703503 or http://arXiv.org/abs/math.PR/0703503 or by email in unzipped form by transmitting an empty message with subject line uget 0703503 or in gzipped form by using subject line get 0703503 to: math(a)arXiv.org.

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Abstract of a paper by Stefan Neuwirth
by Dale Alspach 10 Mar '07

10 Mar '07

This is an announcement for the paper "The maximum modulus of a trigonometric trinomial" by Stefan Neuwirth. Abstract: Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda. Archive classification: Functional Analysis; Classical Analysis and ODEs Mathematics Subject Classification: MSC Primary 30C10, 42A05, 42A45, 46B20; Secondary 26D05, 42A55, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0703236 or http://arXiv.org/abs/math.FA/0703236 or by email in unzipped form by transmitting an empty message with subject line uget 0703236 or in gzipped form by using subject line get 0703236 to: math(a)arXiv.org.

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CONFERENCE ANNOUNCEMENT ICAT08
by ganastss＠memphis.edu 09 Mar '07

09 Mar '07

DEAR COLEAQUES HI! PROFESSOR PAUL BUTZER OF AACHEN TECH.INST.,GERMANY,ONE OF THE MAIN RESEARCHERS OF APPROXIMATION THEORY AND MANY OTHER FIELDS, SUCH AS SAMPLING THEORY/SIGNAL THEORY,FRACTIONAL CALCULUS/ANALYSIS,OPERATORS,SEMIGROUPS, CELEBRATES HIS 80TH BIRTHDAY IN 2008. PROF.BUTZER STILL IS VERY ACTIVE IN RESEARCH AND IN EXCELLENT HEALTH. TO HONOR HIM,HERE AT THE UNIV. OF MEMPHIS,TN,USA WE ORGANISE AN INTERNATIONAL CONFERENCE ON APPROXIMATION THEORY:ALL TOPICS, AND RELATED FIELDS ,SUCH AS INEQUALITIES,FRACTIONAL CALCULUS,FUZZY APPROX.TH,PROBABILISTIC APPROX.TH.,ETC. THE CONFERENCE(ICAT08) WILL BE DURING OCTOBER 11-13,2008. WE HOPE YOU COME,THERE WILL BE PROCEEDINGS. THIS IS THE VERY FIRST ANNOUNCEMENT.THERE WILL BE A WEB SITE SOON. AT THE MOMENT WE COLLECT ONLY INTEREST TO POSSIBLY COME. PLEASE ANSWER US SOON IF YOU MAY BE COME. THANKS CORDIALLY THE ORGANIZER George A. Anastassiou,Ph.D Professor of Mathematics Department of Mathematical Sciences The University of Memphis,Memphis,TN 38152,USA Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series: Concrete & Applicable Math. Springer Consultant-Editor in computational math books Birkhauser Consultant Editor in A.M.Sci. CRC-A.M. Advisor NOVA MATH books ADVISOR ganastss(a)memphis.edu http://www.eudoxuspress.com http://www.msci.memphis.edu/~ganastss/jocaaa http://www.msci.memphis.edu/~ganastss/jcaam http://www.msci.memphis.edu/~ganastss/jafa tel:(INT 001)- 901-678-3144 office 901-751-3553 home 901-678-2482 secr. Fax: 901-678-2480 Associate Editor in: J.Communications in Applied Analysis, Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO, J.Advances in non-linear Variational Inequalities, e-J.of Inequalities in Pure and Applied Math., Anals U.Oradea-Fasciola Mathematica, Archives of Inequalities and Applications, Inter.J.of Pure&Appl.Math.,MIA, Inter.J.of Computational and Numerical Analysis with Appl. Honorary President of Soc.for study & promotion of Ancient Greek Mathematics. Honorary Editor Australian Journal of Mathematical Analysis and Appl. Panamerican Mathematical Journal Eudoxus Press,LLC Pres.

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Call for papers for Banach J. Math.
by Dale Alspach 21 Feb '07

21 Feb '07

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Call for Papers for Banach J. Math. [apologies for multiple postings] Dear ISDE Members, It is my pleasure to invite you most cordially to submit your original research papers or critical survey articles (within the scope of the Journal) for possible publication in "Banach Journal of Mathematics (BJM)" and to promote our journal among your fellow-workers and colleagues. A publishing of your paper will contribute so much for the success of the journal. Following (and attached), kindly find more information about how/where to submit a paper. Kindly visit: http://www.math-analysis.org (an updated mirror) We are looking forward to receiving your contributions in the style file of BJM. Sincerely yours Mohammad Sal Moslehian Editor-in-chief of BJM Address: Department of Mathematics, P. O. Box 1159, Ferdowsi University, Mashhad 91775, Iran Tel-Fax: (+98)(511)(8828606) Fax: (+98)(511)(8828609) E-mail: moslehian(a)member.ams.org Home: http://profsite.um.ac.ir/~moslehian/

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Abstract of a paper by Zhenglu Jiang and Xiaoyong Fu
by Dale Alspach 20 Feb '07

20 Feb '07

This is an announcement for the paper "The Banach-Saks Property of the Banach product spaces" by Zhenglu Jiang and Xiaoyong Fu. Abstract: In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 40H05, 40G05, 47F05 Remarks: 6 The source file(s), bs0206.tex: 25085 bytes, is(are) stored in gzipped form as 0702538.gz with size 8kb. The corresponding postcript file has gzipped size 91kb. Submitted from: mcsjzl(a)mail.sysu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702538 or http://arXiv.org/abs/math.FA/0702538 or by email in unzipped form by transmitting an empty message with subject line uget 0702538 or in gzipped form by using subject line get 0702538 to: math(a)arXiv.org.

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Abstract of a paper by Zhenglu Jiang and Xiaoyong Fu
by Dale Alspach 20 Feb '07

20 Feb '07

This is an announcement for the paper "The weak Banach-Saks Property of the Space $(L_\mu^p)^m$" by Zhenglu Jiang and Xiaoyong Fu. Abstract: In this paper we show the weak Banach-Saks property of the Banach vector space $(L_\mu^p)^m$ generated by $m$ $L_\mu^p$-spaces for $1\leq p<+\infty,$ where $m$ is any given natural number. When $m=1,$ this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of a vector space ${\bf R}^m$ and vector-valued functions in a weakly compact subset of the space $(L_\mu^p)^m$ for $1\leq p<+\infty$ and inequalities when these vector-valued functions are in a weakly* compact subset of the product space $(L_\mu^\infty)^m$ generated by $m$ $L_\mu^\infty$-spaces. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 40H05, 40G05, 47F05 Remarks: 7 The source file(s), jf-bs.tex: 29847 bytes, is(are) stored in gzipped form as 0702537.gz with size 8kb. The corresponding postcript file has gzipped size 104kb. Submitted from: mcsjzl(a)mail.sysu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702537 or http://arXiv.org/abs/math.FA/0702537 or by email in unzipped form by transmitting an empty message with subject line uget 0702537 or in gzipped form by using subject line get 0702537 to: math(a)arXiv.org.

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Abstract of a paper by Florent Baudier and Gilles Lancien
by Dale Alspach 12 Feb '07

12 Feb '07

This is an announcement for the paper "Embeddings of locally finite metric spaces into Banach spaces" by Florent Baudier and Gilles Lancien. Abstract: We show that if X is a Banach space without cotype, then every locally finite metric space embeds metrically into X. Archive classification: Metric Geometry; Functional Analysis Mathematics Subject Classification: 46B20; 51F99 Remarks: 6 pages, to appear in Proceedings of the AMS The source file(s), baudierlancien-final2.tex: 15038 bytes, is(are) stored in gzipped form as 0702266.gz with size 5kb. The corresponding postcript file has gzipped size 75kb. Submitted from: florent.baudier(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0702266 or http://arXiv.org/abs/math.MG/0702266 or by email in unzipped form by transmitting an empty message with subject line uget 0702266 or in gzipped form by using subject line get 0702266 to: math(a)arXiv.org.

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Abstract of a paper by Limor Ben-Efraim and Francoise Lust-Piquard
by Dale Alspach 09 Feb '07

09 Feb '07

This is an announcement for the paper "Poincar\'{e} type inequalities on the discrete cube and in the CAR algebra" by Limor Ben-Efraim and Francoise Lust-Piquard. Abstract: We prove Lp Poincare inequalities for functions on the discrete cube and their discrete gradient. We thus recover an exponential inequality and the concentration phenomenon for the uniform probability on the cube first obtained by Bobkov and Gotze. Inequalities involving the discrete gradient and powers of the discrete Laplacian are also considered, for the Lp norm or more general ones. Similar results hold true, replacing functions on the cube by elements of the CAR algebra and considering the annihilation operators and the number operator. Archive classification: Functional Analysis Mathematics Subject Classification: 46E39, 46L57, 46L51 The source file(s), poincare-cube-final.tex: 85518 bytes, is(are) stored in gzipped form as 0702233.gz with size 21kb. The corresponding postcript file has gzipped size 182kb. Submitted from: limor_be(a)cs.huji.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702233 or http://arXiv.org/abs/math.FA/0702233 or by email in unzipped form by transmitting an empty message with subject line uget 0702233 or in gzipped form by using subject line get 0702233 to: math(a)arXiv.org.

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Abstract of a paper by Denka Kutzarova, Denny Leung, Antonis Manoussakis and Wee Kee Tang
by Dale Alspach 09 Feb '07

09 Feb '07

This is an announcement for the paper "Minimality properties of Tsirelson type spaces" by Denka Kutzarova, Denny Leung, Antonis Manoussakis and Wee Kee Tang. Abstract: In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (e_k) is said to be subsequentially minimal if for every normalized block basis (x_k) of (e_k), there is a further block (y_k) of (x_k) such that (y_k) is equivalent to a subsequence of (e_k). Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal and connections with Bourgain's \ell^{1}-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense. Archive classification: Functional Analysis The source file(s), SubseqMinimal8A.tex: 107238 bytes, is(are) stored in gzipped form as 0702210.gz with size 27kb. The corresponding postcript file has gzipped size 176kb. Submitted from: matlhh(a)nus.edu.sg The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702210 or http://arXiv.org/abs/math.FA/0702210 or by email in unzipped form by transmitting an empty message with subject line uget 0702210 or in gzipped form by using subject line get 0702210 to: math(a)arXiv.org.

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Abstract of a paper by Peter G. Casazza, Gitta Kutyniok, Darrin Speegle and Janet C. Tremain
by Dale Alspach 09 Feb '07

09 Feb '07

This is an announcement for the paper "A decomposition theorem for frames and the Feichtinger conjecture" by Peter G. Casazza, Gitta Kutyniok, Darrin Speegle and Janet C. Tremain. Abstract: In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in $C^{*}$-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the conjecture that every unit norm Bessel sequence is a finite union of frame sequences. 2. Every unit norm Bessel sequence is a finite union of sets each of which is $\omega$-independent for $\ell_2$-sequences. Archive classification: Functional Analysis Mathematics Subject Classification: 46C05; 42C15; 46L05 Remarks: 10 pages The source file(s), Decomposition_PAMS_final.tex: 35701 bytes, proc-l.cls: 2486 bytes, is(are) stored in gzipped form as 0702216.tar.gz with size 12kb. The corresponding postcript file has gzipped size 89kb. Submitted from: gitta.kutyniok(a)math.uni-giessen.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702216 or http://arXiv.org/abs/math.FA/0702216 or by email in unzipped form by transmitting an empty message with subject line uget 0702216 or in gzipped form by using subject line get 0702216 to: math(a)arXiv.org.

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