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|a 1159685257
|a 1163871775
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|a HCDD
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|a Israel Seminar on Geometrical Aspects of Functional Analysis
|d (2017-2019 :
|c Israel)
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|a Geometric aspects of functional analysis :
|b Israel Seminar (GAFA) 2017-2019.
|n Volume I /
|c edited by Bo'az Klartag, Emanuel Milman.
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|a GAFA
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|a Cham :
|b Springer,
|c 2020.
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|a 1 online resource (346 pages)
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|a text
|b txt
|2 rdacontent
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|a computer
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|2 rdamedia
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|a text file
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|b PDF
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|a Lecture Notes in Mathematics Ser. ;
|v v. 2256
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|a Print version record.
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|a Intro -- Preface -- Jean Bourgain: In Memoriam -- Contents Overview for Volume II -- Contents -- 1 Gromov's Waist of Non-radial Gaussian Measures and Radial Non-Gaussian Measures -- 1.1 Introduction -- 1.2 Nonradial Gaussian Measures: Proof of Theorem 1.1.1 -- 1.3 Existence of Waist Theorems for Some Radial Measures -- 1.4 Waist for Radial Measures and Odd Maps -- 1.5 Neighborhoods of Critical Submanifolds -- 1.5.1 Neighborhoods of Submanifolds in the Euclidean Space -- 1.5.2 Neighborhoods in the Sphere and the Complex Projective Space -- 1.6 Appendix: Explanation of the Caffarelli Theorem
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|a 1.7 Appendix: Explanation of the Pancake Decomposition -- 1.7.1 General Version of the Equipartition Argument -- 1.7.2 Modification of the Equipartition Argument for the Spherical Waist Theorem -- 1.7.3 Simplified Version of the Equipartition Argument -- 1.7.4 Proof that the Parts Are Pancakes -- References -- 2 Zhang's Inequality for Log-Concave Functions -- 2.1 Introduction -- 2.2 Notation and Preliminaries -- 2.3 Proof of the Inequality in Theorem 2.1.1 -- 2.4 Characterization of the Equality in Theorem 2.1.1 -- References -- 3 Bobkov's Inequality via Optimal Control Theory
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|a 3.1 Bobkov's Inequality -- 3.2 Bellman Principle -- 3.3 The Proof -- 3.3.1 Hamilton-Jacobi-Bellman PDE -- 3.3.2 Deriving Bobkov's Inequality -- 3.3.3 Optimizers -- References -- 4 Arithmetic Progressions in the Trace of Brownian Motionin Space -- 4.1 Introduction -- 4.2 Proofs -- Reference -- 5 Edgeworth Corrections in Randomized Central Limit Theorems -- 5.1 Introduction -- 5.2 Construction of Asymptotic Expansions -- 5.3 Moments and Deviations of Lyapunov Coefficients -- 5.4 Upper Bounds on Characteristic Functions -- 5.5 Proof of Theorem 5.1.1 -- 5.6 General Lower Bounds
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|a 5.7 Approximation by Mean Characteristic Functions -- 5.8 Proof of Theorem 5.1.2 -- References -- 6 Three Applications of the Siegel Mass Formula -- 6.1 Background on the Siegel Mass Formula -- 6.2 Uneven Parsell-Vinogradov Sums -- 6.3 Non-congruent Tetrahedra in the Truncated Lattice [0,q]3Z3 -- 6.4 Distribution of Lattice Points on Caps -- References -- 7 Decouplings for Real Analytic Surfaces of Revolution -- 7.1 Background and the Main Result -- 7.2 A Case Analysis Based on Principal Curvatures -- 7.3 The Case of the Quasi-Torus -- 7.4 The Perturbed Cone -- 7.5 Final Remarks -- References
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|a 8 On Discrete Hardy-Littlewood Maximal Functions over the Balls in Zd: Dimension-Free Estimates -- 8.1 Introduction -- 8.1.1 Motivations and Statement of the Results -- 8.1.2 The Large-Scale Case -- 8.1.3 The Intermediate-Scale Case -- 8.1.4 The Small-Scale Case -- 8.1.5 Notation -- 8.2 Estimates for the Dyadic Maximal Function: Intermediate Scales -- 8.2.1 Some Preparatory Estimates -- 8.2.2 Analysis on Permutation Groups -- 8.2.3 A Decrease Dimension Trick -- 8.2.4 All Together -- 8.3 Estimates for the Dyadic Maximal Function: Small Scales -- 8.3.1 Some Preparatory Estimates
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|a 8.3.2 Analysis Exploiting the Krawtchouk Polynomials
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|a Continuing the theme of the previous volume, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn-Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
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|a Functional analysis
|v Congresses.
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|a Functional differential equations
|x Asymptotic theory
|v Congresses.
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|a Ecuaciones funcionales
|x Teoría asintótica
|2 embne
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|a Análisis funcional
|2 embne
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|a Functional analysis
|2 fast
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|a Functional differential equations
|x Asymptotic theory
|2 fast
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|a proceedings (reports)
|2 aat
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|a Conference papers and proceedings
|2 fast
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|a Conference papers and proceedings.
|2 lcgft
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|a Actes de congrès.
|2 rvmgf
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|a Milman, Emanuel,
|d 1977-
|1 https://id.oclc.org/worldcat/entity/E39PCjtJwDccJJxtf9XVBJFbtX
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|a Klartag, Bo'az.
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|i has work:
|a Geometric aspects of functional analysis (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGvMXjhHqTmvtQwJ3fQxym
|4 https://id.oclc.org/worldcat/ontology/hasWork
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|i Print version:
|a Milman, Emanuel.
|t Geometric Aspects of Functional Analysis : Israel Seminar (GAFA) 2017-2019 Volume I.
|d Cham : Springer International Publishing AG, ©2020
|z 9783030360191
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| 830 |
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|a Lecture notes in mathematics (Springer-Verlag) ;
|v 2256.
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| 856 |
4 |
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-030-36020-7
|y Click for online access
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|a SPRING-MATH2020
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| 994 |
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|a 92
|b HCD
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