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Geometric Aspects of Functional Analysis

Israel Seminar 1996-2000

  • Book
  • © 2000

Overview

Editors:
  1. Vitali D. Milman
  2. Gideon Schechtman

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1745)

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About this book

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 (21 chapters)

  1. Front Matter

    Pages N2-VIII
    Download chapter PDF

  2. The transportation cost for the cube

    • M. Anttila
    Pages 1-11

  3. The uniform concentration of measure phenomenon in ℓ n p (1 ≤ p ≤ 2)

    • J. Arias-de-Reyna, R. Villa
    Pages 13-18

  4. An editorial comment on the preceding paper

    • G. Schechtman
    Pages 19-20

  5. A remark on the slicing problem

    • K. Ball
    Pages 21-26

  6. Remarks on the growth of L p-norms of polynomials

    • S. G. Bobkov
    Pages 27-35

  7. Positive lyapounov exponents for most energies

    • J. Bourgain
    Pages 37-66

  8. Anderson localization for the band model

    • J. Bourgain, S. Jitomirskaya
    Pages 67-79

  9. Convex bodies with minimal mean width

    • A. A. Giannopoulos, V. D. Milman, M. Rudelson
    Pages 81-93

  10. Euclidean projections of a p-convex body

    • O. Guédon, A. E. Litvak
    Pages 95-108

  11. Remarks on minkowski symmetrizations

    • B. Klartag
    Pages 109-117

  12. Average volume of sections of star bodies

    • A. Koldobsky, M. Lifshits
    Pages 119-146

  13. Between sobolev and poincaré

    • R. Latała, K. Oleszkiewicz
    Pages 147-168

  14. Random aspects of high-dimensional convex bodies

    • A. E. Litvak, N. Tomczak-Jaegermann
    Pages 169-190

  15. A geometric lemma and duality of entropy numbers

    • V. D. Milman, S. J. Szarek
    Pages 191-222

  16. Stabilized asymptotic structures and envelopes in banach spaces

    • V. D. Milman, N. Tomczak-Jaegermann
    Pages 223-237

  17. On the isotropic constant of Non-symmetric convex bodies

    • G. Paouris
    Pages 239-243

  18. Concentration on the ℓ n p ball

    • G. Schechtman, J. Zinn
    Pages 245-256

  19. Shannon’s entropy power inequality via restricted minkowski sums

    • S. J. Szarek, D. Voiculescu
    Pages 257-262

  20. Notes on an inequality by pisier for functions on the discrete cube

    • R. Wagner
    Pages 263-268
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