Banach March 2007

banach@mathdept.okstate.edu

2 participants
5 discussions

Abstract of a paper by Dumitru Popa
by Dale Alspach 22 Mar '07

22 Mar '07

This is an announcement for the paper "Khinchin's inequality, Dunford--Pettis and compact operators on the space $\pmb{C([0,1],X)}$" by Dumitru Popa. Abstract: We prove that if $X,Y$ are Banach spaces, $\Omega$ a compact Hausdorff space and $U\hbox{\rm :}\ C(\Omega,X)\rightarrow Y$ is a bounded linear operator, and if $U$ is a Dunford--Pettis operator the range of the representing measure $G(\Sigma) \subseteq DP(X,Y)$ is an uniformly Dunford--Pettis family of operators and $\|G\|$ is continuous at $\emptyset$. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space $C([0,1],X)$ with values in $c_{0}$ or $l_{p}$, ($1\leq p<\infty$) be Dunford--Pettis and/or compact operators, in which, Khinchin's inequality plays an important role. Archive classification: Functional Analysis Mathematics Subject Classification: 46B28; 47A80; 47B10 Remarks: 18 pages The source file(s), mat01.cls: 37299 bytes, mathtimy.sty: 20 bytes, pm2710new.tex: 66481 bytes, is(are) stored in gzipped form as 0703626.tar.gz with size 24kb. The corresponding postcript file has gzipped size 76kb. Submitted from: dpopa(a)univ-ovidius.ro The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0703626 or http://arXiv.org/abs/math.FA/0703626 or by email in unzipped form by transmitting an empty message with subject line uget 0703626 or in gzipped form by using subject line get 0703626 to: math(a)arXiv.org.

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Abstract of a paper by Andrea Colesanti
by Dale Alspach 21 Mar '07

21 Mar '07

This is an announcement for the paper "From the Brunn-Minkowski inequality to a class of Poincar\'e type inequalities" by Andrea Colesanti. Abstract: We present an argument which leads from the Brunn-Minkowski inequality to a Poincare' type inequality on the boundary of convex bodies with smooth boundary and positive Gauss curvature. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 52A20; 26D10 Remarks: 9 pages The source file(s), testo.tex: 21763 bytes, is(are) stored in gzipped form as 0703584.gz with size 7kb. The corresponding postcript file has gzipped size 93kb. Submitted from: colesant(a)math.unifi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0703584 or http://arXiv.org/abs/math.FA/0703584 or by email in unzipped form by transmitting an empty message with subject line uget 0703584 or in gzipped form by using subject line get 0703584 to: math(a)arXiv.org.

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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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Banach March 2007