자료유형  

 단행본

International Standard Book Number  

9781400842698 (electronic bk.)

International Standard Book Number  

1400842697 (electronic bk.)

International Standard Book Number  

9780691153551 (hbk.)

International Standard Book Number  

0691153558 (hbk.)

International Standard Book Number  

9780691153568 (pbk.)

International Standard Book Number  

0691153566 (pbk.)

Library of Congress Call Number  

QA322.2 .L564 2012

Dewey Decimal Classification Number  

515/.88

Main Entry-Personal Name  

Lindenstrauss, Joram.

Publication, Distribution, etc. (Imprint  

Princeton : Princeton University Press, 2012

Physical Description  

1 online resource (436 p)

Series Statement  

Annals of mathematics studies ; no. 179

General Note  

Description based upon print version of record.

General Note  

14.7 Proof of Theorem

Bibliography, Etc. Note  

Includes bibliographical references and index.

Formatted Contents Note  

완전내용Cover; Title Page; Copyright Page; Table of Contents; Chapter 1. Introduction; 1.1 Key notions and notation; Chapter 2. Gâteaux Dfferentiability of Lipschitz Functions; 2.1 Radon-Nikodým Property; 2.2 Haar and Aronszajn-Gauss Null Sets; 2.3 Existence Results for Gâteaux Derivatives; 2.4 Mean Value Estimates; Chapter 3. Smoothness, Convexity, Porosity, and Separable Determination; 3.1 A criterion of Differentiability of Convex Functions; 3.2 Fréchet Smooth and Nonsmooth Renormings; 3.3 Fréchet Differentiability of Convex Functions; 3.4 Porosity and Nondifferentiability

Formatted Contents Note  

완전내용3.5 Sets of Fréchet Differentiability Points3.6 Separable Determination; Chapter 4. e-Fréchet Differentiability; 4.1 e-Differentiability and Uniform Smoothness; 4.2 Asymptotic Uniform Smoothness; 4.3 e-Fréchet Differentiability of Functions on Asymptotically Smooth Spaces; Chapter 5. G-Null and Gn-Null Sets; 5.1 Introduction; 5.2 G-Null Sets and Gâteaux Differentiability; 5.3 Spaces of Surfaces; 5.4 G- and Gn-Null Sets of low Borel Classes; 5.5 Equivalent Definitions of Gn-Null Sets; 5.6 Separable Determination; Chapter 6. Fréchet Differentiability Except for G-Null Sets; 6.1 Introduction

Formatted Contents Note  

완전내용6.2 Regular Points6.3 A Criterion of Fréchet Differentiability; 6.4 Fréchet Differentiability Except for G-Null Sets; Chapter 7. Variational Principles; 7.1 Introduction; 7.2 Variational Principles via Games; 7.3 Bimetric Variational Principles; Chapter 8. Smoothness and Asymptotic Smoothness; 8.1 Modulus of Smoothness; 8.2 Smooth Bumps with Controlled Modulus; Chapter 9. Preliminaries to Main Results; 9.1 Notation, Linear Operators, Tensor Products; 9.2 Derivatives and Regularity; 9.3 Deformation of Surfaces Controlled by ?n; 9.4 Divergence Theorem; 9.5 Some Integral Estimates

Formatted Contents Note  

완전내용Chapter 10. Porosity, Gn- and G-Null Sets10.1 Porous and s-Porous Sets; 10.2 A Criterion of Gn-nullness of Porous Sets; 10.3 Directional Porosity and Gn-Nullness; 10.4 s-Porosity and Gn-Nullness; 10.5 G1-Nullness of Porous Sets and Asplundness; 10.6 Spaces in which s-Porous Sets are G-Null; Chapter 11. Porosity and e-Fréchet Differentiability; 11.1 Introduction; 11.2 Finite Dimensional Approximation; 11.3 Slices and e-Differentiability; Chapter 12. Fréchet Differentiability of Real-Valued Functions; 12.1 Introduction and Main Results; 12.2 An Illustrative Special Case

Formatted Contents Note  

완전내용12.3 A Mean Value Estimate12.4 Proof of Theorems; 12.5 Generalizations and Extensions; Chapter 13. Fréchet Differentiability of Vector-Valued Functions; 13.1 Main Results; 13.2 Regularity Parameter; 13.3 Reduction to a Special Case; 13.4 Regular Fréchet Differentiability; 13.5 Fréchet Differentiability; 13.6 Simpler Special Cases; Chapter 14. Unavoidable Porous Sets and Nondifferentiable Maps; 14.1 Introduction and Main Results; 14.2 An Unavoidable Porous Set in l1; 14.3 Preliminaries to Proofs of Main Results; 14.4 The Main Construction; 14.5 The Main Construction; 14.6 Proof of Theorem

Summary, Etc.  

요약This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis.

Subject Added Entry-Topical Term  

Mathematics

Subject Added Entry-Topical Term  

Banach spaces

Subject Added Entry-Topical Term  

Calculus of variations

Subject Added Entry-Topical Term  

Functional analysis

Subject Added Entry-Topical Term  

MATHEMATICS / Calculus.

Subject Added Entry-Topical Term  

MATHEMATICS / Mathematical Analysis.

Added Entry-Personal Name  

Preiss, David.

Added Entry-Personal Name  

Tiaer, Jaroslav.

Additional Physical Form Entry  

Print version / Lindenstrauss, JoramFrechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces. Princeton : Princeton University Press,c2012. 9780691153568

Electronic Location and Access  

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Control Number  

joongbu:397209