omitir hasta el contenido
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces Ver este material de antemano
CerrarVer este material de antemano
Chequeando…

Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Autor: Joram Lindenstrauss; David Preiss; Jaroslav Tišer
Editorial: Princeton : Princeton University Press, 2012.
Serie: Annals of mathematics studies, no. 179
Edición/Formato:   Libro-e : Documento : Inglés (eng)Ver todas las ediciones y todos los formatos
Base de datos:WorldCat
Resumen:
This 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  Leer más
Calificación:

(todavía no calificado) 0 con reseñas - Ser el primero.

Temas
Más materiales como éste

 

Encontrar un ejemplar en línea

Enlaces a este material

Encontrar un ejemplar en la biblioteca

&AllPage.SpinnerRetrieving; Encontrando bibliotecas que tienen este material…

Detalles

Género/Forma: Electronic books
Formato físico adicional: Print version:
Lindenstrauss, Joram.
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces.
Princeton : Princeton University Press, ©2012
Tipo de material: Documento, Recurso en Internet
Tipo de documento: Recurso en Internet, Archivo de computadora
Todos autores / colaboradores: Joram Lindenstrauss; David Preiss; Jaroslav Tišer
ISBN: 9781400842698 1400842697
Número OCLC: 769343169
Notas: 14.7 Proof of Theorem.
Descripción: 1 online resource (436 pages).
Contenido: Cover; 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. 3.5 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. 6.2 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. Chapter 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. 12.3 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.
Título de la serie: Annals of mathematics studies, no. 179

Resumen:

Focuses on the difficult question of existence of Frchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. This book provides a bridge between descriptive set theory and  Leer más

Reseñas

Reseñas editoriales

Resumen de la editorial

"The book is well written--as one would expect from its distinguished authors, including the late Joram Lindestrauss (1936-2012). It contains many fascinating and profound results. It no doubt will Leer más

 
Reseñas contribuidas por usuarios
Recuperando reseñas de GoodReads…
Recuperando reseñas de DOGObooks…

Etiquetas

Ser el primero.

Materiales similares

Temas relacionados:(7)

Listas de usuarios con este material (1)

Confirmar este pedido

Ya ha pedido este material. Escoja OK si desea procesar el pedido de todos modos.

Datos enlazados


<http://www.worldcat.org/oclc/769343169>
library:oclcnum"769343169"
library:placeOfPublication
library:placeOfPublication
owl:sameAs<info:oclcnum/769343169>
rdf:typeschema:Book
schema:about
schema:about
<http://id.worldcat.org/fast/844140>
rdf:typeschema:Intangible
schema:name"Calculus of variations"@en
schema:name"Calculus of variations."@en
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:bookFormatschema:EBook
schema:contributor
schema:contributor
schema:creator
schema:datePublished"2012"
schema:description"Cover; 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."@en
schema:description"This 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. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics."@en
schema:exampleOfWork<http://worldcat.org/entity/work/id/1029425488>
schema:genre"Electronic books."@en
schema:inLanguage"en"
schema:name"Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces"@en
schema:publisher
schema:url<http://www.myilibrary.com?id=337995>
schema:url<http://www.jstor.org/stable/10.2307/j.ctt7svpc>
schema:url
schema:url<http://public.eblib.com/choice/publicfullrecord.aspx?p=827806>
schema:url<http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=421487>
schema:workExample

Content-negotiable representations

Cerrar ventana

Inicie una sesión con WorldCat 

¿No tienes una cuenta? Puede fácilmente crear una cuenta gratuita.