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Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar 1996- Vitali D. Milman,Gideon Schechtman Book 2000 Springer-Verlag Berlin Heidelbe

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书目名称Geometric Aspects of Functional Analysis
副标题Israel Seminar 1996-
编辑Vitali D. Milman,Gideon Schechtman
视频video
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Geometric Aspects of Functional Analysis; Israel Seminar 1996- Vitali D. Milman,Gideon Schechtman Book 2000 Springer-Verlag Berlin Heidelbe
描述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.
出版日期Book 2000
关键词Banach space; Dimension; Power; Trend; asymptotic geometric analysis; convexity; functional analysis; local
版次1
doihttps://doi.org/10.1007/BFb0107201
isbn_softcover978-3-540-41070-6
isbn_ebook978-3-540-45392-5Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2000
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Anderson localization for the band model,orresponding to the band model ℤ × {1, ..., .}. Recall that ‘Anderson localization’ means pure point spectrum with exponentially decaying eigenfunctions. We also discuss the issue of dynamical localization.
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Euclidean projections of a ,-convex body,sts a projection of rank . with the distance to the Euclidean ball not exceeding ..(./ln(1 + .))., where .. is an absolute positive constant depending only on .. Moreover, we obtain precise estimates of entropy numbers of identity operator acting between ℓ. and ℓ. spaces for the case 0 < . < . ≤ ∞.
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Remarks on minkowski symmetrizations,ed ball, if we start from an arbitrary convex body in ℝ.. We also show that the number of “deterministic” symmetrizations needed to approximate an Euclidean ball may be significantly smaller than the number of “random” ones.
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Average volume of sections of star bodies,te the precise asymptotics of the average volume of central sections and then prove a concentration inequality of exponential type. For the case of non-central hyperplane sections of the cube, we prove a local limit theorem confirming the conjecture on the asymptotically Gaussian dependence of the v
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,Between sobolev and poincaré, space (.., ‖ · ‖). We prove that there exists a universal constant . such that for any smooth real function . on .. and any . ∈ [1,2) .. We prove also that if for some probabilistic measure . on .. the above inequality is satisfied for any . ∈ [1, 2) and any smooth . then for any . : .. → . such th
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Stabilized asymptotic structures and envelopes in banach spaces,
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