Banach January 2008

banach@mathdept.okstate.edu

4 participants
8 discussions

Postdoctoral position at Case Western Reserve University
by Stanislaw J. Szarek 29 Jan '08

29 Jan '08

Department of Mathematics at Case Western Reserve University invites applications for a post-doctoral position starting in the fall of 2008. The position is funded by the NSF Focused Research Group grant "Collaborative Research: Fourier analytic and probabilistic methods in geometric functional analysis and convexity" (see http://www.math.ucdavis.edu/~geofunction). We seek applicants in the area of functional analysis, convexity theory and related high-dimensional phenomena, the direction that recently has been often referred to as ``asymptotic geometric analysis" and of which members of the Department are internationally recognized leaders. See http://www.cwru.edu/artsci/math/szarek/ and http://www.cwru.edu/artsci/math/werner/ for examples of recent research directions. The starting date of the appointment is somewhat flexible, as is the profile: it may involve either 100% effort commitment to the grant (no teaching duties), or an effort split between the grant and teaching (see http://www.case.edu/artsci/math/employment.htm under "Other Searches: Mathematics: Lecturer"). The appointment is initially budgeted for one year, but longer durations under the split effort scenario may be considered. Applicants should submit a letter of application, AMS cover sheet, CV, and have three letters of evaluation sent, preferably by email to math-faculty-position(a)cwru.edu, with copies to szarek(a)cwru.edu and elisabeth.werner(a)case.edu. Applications received by February 15, 2008 will receive full consideration; applications will be accepted until the position is filled. Case is an integral part of one of the major research medical complexes in the country. It also has a major presence in various science and engineering disciplines. Geographically, it is located on the eastern edge of Cleveland, in northeast Ohio, adjacent to University Circle, home to the Cleveland Symphony Orchestra, the Cleveland Museum of Art, and many other cultural institutions. There is a wide variety of housing, schooling, and other amenities nearby. Case Western Reserve University is committed to diversity and is an affirmative action, equal opportunity employer. Applications from women or minorities are especially encouraged.

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Abstract of a paper by Philippe Jaming, Mate Matolcsi, and Szilard Gy. Revesz
by alspach＠fourier.math.okstate.edu 22 Jan '08

22 Jan '08

This is an announcement for the paper "On the extremal rays of the cone of positive, positive definite functions" by Philippe Jaming, Mate Matolcsi, and Szilard Gy. Revesz. Abstract: The aim of this paper is to investigate the cone of non-negative, radial, positive-definite functions in the set of continuous functions on $\R^d$. Elements of this cone admit a Choquet integral representation in terms of the extremals. The main feature of this article is to characterize some large classes of such extremals. In particular, we show that there many other extremals than the gaussians, thus disproving a conjecture of G. Choquet and that no reasonable conjecture can be made on the full set of extremals. The last feature of this article is to show that many characterizations of positive definite functions available in the literature are actually particular cases of the Choquet integral representations we obtain. Archive classification: math.CA math.FA math.PR Mathematics Subject Classification: 42A82 The source file(s), domain.eps: 12230 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.0941 or http://arXiv.org/abs/0801.0941 or by email in unzipped form by transmitting an empty message with subject line uget 0801.0941 or in gzipped form by using subject line get 0801.0941 to: math(a)arXiv.org.

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Abstract of a paper by Sonja Cox and Mark Veraar
by alspach＠fourier.math.okstate.edu 22 Jan '08

22 Jan '08

This is an announcement for the paper "Some remarks on tangent martingale difference sequences in $L^1$-spaces" by Sonja Cox and Mark Veraar. Abstract: Let $X$ be a Banach space. Suppose that for all $p\in (1, \infty)$ a constant $C_{p,X}$ depending only on $X$ and $p$ exists such that for any two $X$-valued martingales $f$ and $g$ with tangent martingale difference sequences one has \[\E\|f\|^p \leq C_{p,X} \E\|g\|^p \ \ \ \ \ \ (*).\] This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either $f$ or $g$ satisfy the so-called (CI) condition. However, for some applications it suffices to assume that $(*)$ holds whenever $g$ satisfies the (CI) condition. We show that the class of Banach spaces for which $(*)$ holds whenever only $g$ satisfies the (CI) condition is more general than the class of UMD spaces, in particular it includes the space $L^1$. We state several problems related to $(*)$ and other decoupling inequalities. Archive classification: math.PR math.FA Mathematics Subject Classification: 60B05; 46B09; 60G42 Citation: Electron. Commun. Probab. 12, 421-433, (2007) The source file(s), tangent_arxiv.tex: 47306 bytes, is(are) stored in gzipped form as 0801.0695.gz with size 13kb. The corresponding postcript file has gzipped size 101kb. Submitted from: mark(a)profsonline.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.0695 or http://arXiv.org/abs/0801.0695 or by email in unzipped form by transmitting an empty message with subject line uget 0801.0695 or in gzipped form by using subject line get 0801.0695 to: math(a)arXiv.org.

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Abstract of a paper by Gestur Olafsson and Boris Rubin
by alspach＠fourier.math.okstate.edu 20 Jan '08

20 Jan '08

This is an announcement for the paper "Invariant functions on Grassmannians" by Gestur Olafsson and Boris Rubin. Abstract: It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces dimension of its actual argument, hold for every compact symmetric space and can be obtained in the framework of Lie-theoretic consideration. In the present article, this phenomenon is given precise meaning for functions on the Grassmann manifold $G_{n,i}$ of $i$-dimensional subspaces of $\bbr^n$, which are invariant under orthogonal transformations preserving complementary coordinate subspaces of arbitrary fixed dimension. The corresponding integral formulas are obtained. Our method relies on bi-Stiefel decomposition and does not invoke Lie theory. Archive classification: math.FA Mathematics Subject Classification: 44A12; 52A38 Remarks: 11 pages The source file(s), GOBR_8_arxiv.tex: 39436 bytes, is(are) stored in gzipped form as 0801.0081.gz with size 14kb. The corresponding postcript file has gzipped size 89kb. Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.0081 or http://arXiv.org/abs/0801.0081 or by email in unzipped form by transmitting an empty message with subject line uget 0801.0081 or in gzipped form by using subject line get 0801.0081 to: math(a)arXiv.org.

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Abstract of a paper by Heinz H. Bauschke, Xianfu Wang, Jane Ye, and Xiaoming Yuan
by alspach＠fourier.math.okstate.edu 18 Jan '08

18 Jan '08

This is an announcement for the paper "Bregman distances and Chebyshev sets" by Heinz H. Bauschke, Xianfu Wang, Jane Ye, and Xiaoming Yuan. Abstract: A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show that if every point in the space has a unique nearest point in a closed set, then the set is convex. We provide two approaches: one is by nonsmooth analysis; the other by maximal monotone operator theory. Subdifferentiability properties of Bregman nearest distance functions are also given. Archive classification: math.FA Mathematics Subject Classification: Primary 41A65; Secondary 47H05, 49J52. The source file(s), submitted.tex: 67922 bytes, is(are) stored in gzipped form as 0712.4030.gz with size 19kb. The corresponding postcript file has gzipped size 134kb. Submitted from: heinz.bauschke(a)ubc.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0712.4030 or http://arXiv.org/abs/0712.4030 or by email in unzipped form by transmitting an empty message with subject line uget 0712.4030 or in gzipped form by using subject line get 0712.4030 to: math(a)arXiv.org.

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AMAT08
by George A Anastassiou (ganastss) 17 Jan '08

17 Jan '08

DEAR COLLEAQUES HI! CONFERENCE ANNOUNCEMENT: "International Conference on Applied Mathematics and Approximation Theory 2008", October 11-13,2008, University of Memphis, Memphis, TN, USA. Honoring 80th Birthday of P.L.Butzer (AMAT08). Plenary Speakers:C.Bardaro, J.Bona, B.Berndt, F.Deutsch, K.Diethelm, S.Dragomir, J.Goldstein, M.Ismail, M.J.Lai, H.Mhaskar, J.Prestin, S.Samko, R.Stens, A.Zayed. Organizer:George Anastassiou, http://www.msci.memphis.edu/AMAT2008/ PLEASE REGISTER-COME THANKS SINCERELY YOURS George A. Anastassiou,Ph.D DOCTOR HONORIS CAUSA 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<mailto:ganastss@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, Journal of Inequalities and Applications, Inter.J.of Pure&Appl.Math.,MIA, Inter.J.of Computational and Numerical Analysis with Appl. President of World Soc.for study & promotion of Ancient Greek Mathematics Honorary Editor Australian Journal of Mathematical Analysis and Appl. Panamerican Mathematical Journal Eudoxus Press,LLC Pres.,ETC.

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Abstract of a paper by Emanuel Milman
by alspach＠fourier.math.okstate.edu 16 Jan '08

16 Jan '08

This is an announcement for the paper "On the role of convexity in isoperimetry, spectral-gap and concentration" by Emanuel Milman. Abstract: We show that for convex domains in Euclidean space, Cheeger's isoperimetric inequality, Spectral-Gap of the Neumann Laplacian, Exponential concentration of 1-Lipschitz functions, and the a-priori weakest linear tail-decay of 1-Lipschitz functions, are all equivalent (to within universal constants). This substantially extends previous results of Maz'ya, Cheeger, Gromov--Milman, Buser and Ledoux. As an application, we conclude the stability of the Spectral-Gap for convex domains under convex perturbations which preserve volume (up to constants) and under maps which are ``on-average'' Lipschitz. We also easily recover (and extend) many previously known lower bounds, due to Payne--Weinberger, Li--Yau, Kannan--Lov\'asz--Simonovits, Bobkov and Sodin, on the Cheeger constant for convex domains. We also provide a new characterization of the Cheeger constant, as one over the expectation of the distance from the ``worst'' Borel set having half the measure of the convex domain. As a by-product of our methods, we develop a coherent single framework for passing between isoperimetric inequalities, Orlicz-Sobolev functional inequalities and q-capacities, the latter being notions introduced by Maz'ya and extended by Barthe--Cattiaux--Roberto. As an application, we extend the known results due to the latter authors about the stability of the isoperimetric profile under tensorization, when there is no Central-Limit obstruction. A crucial ingredient to our proof is a result from Riemannian Geometry on the concavity of the isoperimetric profile. Our results extend to the more general setting of Riemannian manifolds with density which satisfy the $CD(0,\infty)$ curvature-dimension condition of Bakry-\'Emery. Archive classification: math.MG math.FA Remarks: 70 pages, 1st version The source file(s), Dingir120.eps: 7755 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0712.4092 or http://arXiv.org/abs/0712.4092 or by email in unzipped form by transmitting an empty message with subject line uget 0712.4092 or in gzipped form by using subject line get 0712.4092 to: math(a)arXiv.org.

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Conference on Convex Geometry
by Dale Alspach 04 Jan '08

04 Jan '08

Dear Colleagues, We would like to invite you to participate in the Conference on Convex Geometry in Columbia, Missouri in March 2008. There will be two mini-conferences - Classical Convex Geometry on March 21-23 and Asymptotic Convex Geometry on March 28-30. Please see the conference homepage at http://www.math.missouri.edu/calendar/FRG-08 which contains the list of speakers, accomodations and directions to Columbia, Missouri. Please take a minute to register at the website above. Best regards, Alex Koldobsky and Mark Rudelson

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Banach January 2008