Geometric Aspects of Functional Analysis: Israel Seminar 1996–2000

M. Anttila (auth.), Vitali D. Milman, Gideon Schechtman (eds.)3540410708, 9783540410706

This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.

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Table of contents :
The transportation cost for the cube….Pages 1-11
An editorial comment on the preceding paper….Pages 13-18
A remark on the slicing problem….Pages 19-20
Remarks on the growth of L p -norms of polynomials….Pages 21-26
Positive lyapounov exponents for most energies….Pages 27-35
Anderson localization for the band model….Pages 37-66
Convex bodies with minimal mean width….Pages 67-79
Euclidean projections of a p -convex body….Pages 81-93
Remarks on minkowski symmetrizations….Pages 95-108
Average volume of sections of star bodies….Pages 109-117
Between sobolev and poincaré….Pages 119-146
Random aspects of high-dimensional convex bodies….Pages 147-168
A geometric lemma and duality of entropy numbers….Pages 169-190
Stabilized asymptotic structures and envelopes in banach spaces….Pages 191-222
On the isotropic constant of Non-symmetric convex bodies….Pages 223-237
Shannon’s entropy power inequality via restricted minkowski sums….Pages 239-243
Notes on an inequality by pisier for functions on the discrete cube….Pages 245-256
Seminar talks….Pages 257-262
….Pages 263-268