- Banach - mathdept.okstate.edu

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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Abstract of a paper by Yuri I. Lyubich
by Dale Alspach 08 Dec '07

08 Dec '07

This is an announcement for the paper "Upper bound for isometric embeddings \ell_2^m\to\ell_p^n" by Yuri I. Lyubich. Abstract: The isometric embeddings $\ell_{2;K}^m\to\ell_{p;K}^n$ ($m\geq 2$, $p\in 2\N$) over a field $K\in{R, C, H}$ are considered, and an upper bound for the minimal $n$ is proved. In the commutative case ($K\neq H$) the bound was obtained by Delbaen, Jarchow and Pe{\l}czy{\'n}ski (1998) in a different way. Archive classification: math.FA Mathematics Subject Classification: 46B04 Remarks: 5 pages The source file(s), upbound.bbl: 1810 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0712.0214 or http://arXiv.org/abs/0712.0214 or by email in unzipped form by transmitting an empty message with subject line uget 0712.0214 or in gzipped form by using subject line get 0712.0214 to: math(a)arXiv.org.

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Abstract of a paper by J. G. Christensen and G. Olafsson
by Dale Alspach 08 Dec '07

08 Dec '07

This is an announcement for the paper "Coorbit spaces for dual pairs" by J. G. Christensen and G. Olafsson. Abstract: This paper contains a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Groechenig. This theory has been a powerful tool in characterizing Banach spaces of functions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of $\mathrm{SL}_2(\mathbb{R})$. We suggest a generalization of the coorbit space theory, which is able to account for a wider range of Banach spaces and also for quasi Banach spaces. A few examples of Banach spaces which could not be covered by the previous theory are described. Archive classification: math.FA math.RT Mathematics Subject Classification: 43A15,42B35 (Primary) 22D12 (Secondary) The source file(s), coorbit.bbl: 4205 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0711.4120 or http://arXiv.org/abs/0711.4120 or by email in unzipped form by transmitting an empty message with subject line uget 0711.4120 or in gzipped form by using subject line get 0711.4120 to: math(a)arXiv.org.

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Abstract of a paper by R.Haydon, E.Odell, Th.Schlumprecht
by Dale Alspach 08 Dec '07

08 Dec '07

This is an announcement for the paper "Small subspaces of L_p" by R.Haydon, E.Odell, Th.Schlumprecht. Abstract: We prove that if $X$ is a subspace of $L_p$ $(2<p<\infty)$ then either $X$ embeds isomorphically into $\ell_p \oplus \ell_2$ or $X$ contains a subspace $Y$, which is isomorphic to $\ell_p(\ell_2)$. We also give an intrinsic characterization of when $X$ embeds into $\ell_p \oplus \ell_2$ in terms of weakly null trees in $X$ or equivalently in terms of the ``infinite asymptotic game'' played in $X$. This solves problems concerning small subspaces of $L_p$ originating in the 1970's. The techniques used were developed over several decades, the most recent being that of weakly null trees developed in the 2000's. Archive classification: math.FA Mathematics Subject Classification: 46E30 The source file(s), smallsubspaces.tex: 99982 bytes, is(are) stored in gzipped form as 0711.3919.gz with size 31kb. The corresponding postcript file has gzipped size 185kb. Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0711.3919 or http://arXiv.org/abs/0711.3919 or by email in unzipped form by transmitting an empty message with subject line uget 0711.3919 or in gzipped form by using subject line get 0711.3919 to: math(a)arXiv.org.

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Abstract of a paper by Jarno Talponen
by Dale Alspach 08 Dec '07

08 Dec '07

This is an announcement for the paper "Convex-transitivity and function spaces" by Jarno Talponen. Abstract: It is shown that the Bochner space L^{p}([0,1],X) is convex-transitive for any convex-transitive X and 1\leq p\leq \infty. If H is an infinite-dimensional Hilbert space and C_{0}(L) is convex-transitive, then C_{0}(L,H) is convex-transitive. Some new fairly concrete examples of convex-transitive spaces are provided. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46E40 The source file(s), Rotations3.tex: 62608 bytes, is(are) stored in gzipped form as 0711.3768.gz with size 19kb. The corresponding postcript file has gzipped size 119kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0711.3768 or http://arXiv.org/abs/0711.3768 or by email in unzipped form by transmitting an empty message with subject line uget 0711.3768 or in gzipped form by using subject line get 0711.3768 to: math(a)arXiv.org.

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Conference on Applied Mathematics and Approximation Theory
by Dale Alspach 07 Dec '07

07 Dec '07

“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/

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Summer school on, "Fourier analytic and probabilistic methods in geometric functional, analysis and convexity"
by Artem Zvavitch 04 Dec '07

04 Dec '07

Dear Colleagues, We would like to invite you to participate in the summer school on "Fourier analytic and probabilistic methods in geometric functional analysis and convexity" in August 13-20, 2008. The school is being organized by the NSF funded Focused Research Group collaborative project on the same subject (http://www.math.ucdavis.edu/~geofunction/) It is oriented towards graduate students, postdocs and researchers who wish to get an introduction to the subject. The school will feature several series's of lectures. Confirmed speakers include Alexander Barvinok (University of Michigan), Piotr Indyk (Massachusetts Institute of Technology), Fedor Nazarov (University of Wisconsin-Madison), Krzysztof Oleszkiewicz (University of Warsaw), Rolf Schneider (University of Freiburg), Santosh S. Vempala (Georgia Institute of Technology). The school will be hosted by the Department of Mathematical Sciences at Kent State University in August 13-20, 2008. Kent is located in the suburbs of Cleveland, Ohio, where summers are quite beautiful. We plan to spend one of the evenings at the nearby Blossom Music Center, the summer home of the renowned Cleveland Orchestra. With NSF funding we will be able to cover local, and, probably, travel expenses for a limited number of participants, so we ask you to reply as soon as possible to Dmitry Ryabogin (ryabogin(a)math.kent.edu) or Artem Zvavitch (zvavitch(a)math.kent.edu) Graduate students and Postdoctoral fellows are especially encouraged to apply. For further information and breaking news, please, consult http://www.math.kent.edu/math/FAPR.cfm Again, please note that your early response will help us gauge the needs for housing, lecture room(s), etc. We hope to be sending out information regarding housing by the end of December. We hope to see you in Kent next August. Best Regards, The organizing committee Alex Koldobsky Mark Rudelson Dmitry Ryabogin Stanislaw Szarek Roman Vershynin Elisabeth Werner Artem Zvavitch

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Twp password reminders
by Dale Alspach 01 Dec '07

01 Dec '07

I neglected to shut off the automated password reminder on the old server. The message with hardy.math.okstate.edu at the bottom is the correct one. Sorry for any confusion this may have caused. Dale Alspach

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Abstract of a paper by Haskell P. Rosenthal
by Dale Alspach 04 Nov '07

04 Nov '07

This is an announcement for the paper "Some new characterizations of Banach spaces containing $\ell^1$" by Haskell P. Rosenthal. Abstract: Several new characterizations of Banach spaces containing a subspace isomorphic to $\ell^1$, are obtained. These are applied to the question of when $\ell^1$ embeds in the injective tensor product of two Banach spaces. Archive classification: math.FA Remarks: 27 pages, AMSLaTeX The source file(s), new-char.tex: 120502 bytes, is(are) stored in gzipped form as 0710.5944.gz with size 35kb. The corresponding postcript file has gzipped size 163kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0710.5944 or http://arXiv.org/abs/0710.5944 or by email in unzipped form by transmitting an empty message with subject line uget 0710.5944 or in gzipped form by using subject line get 0710.5944 to: math(a)arXiv.org.

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