Vai al contenuto principale della pagina

Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces [[electronic resource] /] / Joram Lindenstrauss, David Preiss, Jaroslav Tiser



(Visualizza in formato marc)    (Visualizza in BIBFRAME)

Autore: Lindenstrauss Joram <1936-> Visualizza persona
Titolo: Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces [[electronic resource] /] / Joram Lindenstrauss, David Preiss, Jaroslav Tiser Visualizza cluster
Pubblicazione: Princeton, : Princeton University Press, 2012
Edizione: Course Book
Descrizione fisica: 1 online resource (436 p.)
Disciplina: 515/.88
Soggetto topico: Banach spaces
Calculus of variations
Functional analysis
Soggetto non controllato: Asplund space
Banach space
Borel sets
Euclidean space
Frechet differentiability
Fréchet derivative
Fréchet differentiability
Fréchet smooth norm
Gâteaux derivative
Gâteaux differentiability
Hilbert space
Lipschitz function
Lipschitz map
Radon-Nikodým property
asymptotic uniform smoothness
asymptotically smooth norm
asymptotically smooth space
bump
completeness
cone-monotone function
convex function
deformation
derivative
descriptive set theory
flat surface
higher dimensional space
infinite dimensional space
irregular behavior
irregularity point
linear operators
low Borel classes
lower semicontinuity
mean value estimate
modulus
multidimensional mean value
nonlinear functional analysis
nonseparable space
null sets
perturbation function
perturbation game
perturbation
porosity
porous sets
regular behavior
regular differentiability
regularity parameter
renorming
separable determination
separable dual
separable space
slice
smooth bump
subspace
tensor products
three-dimensional space
two-dimensional space
two-player game
variational principle
variational principles
Γ-null sets
ε-Fréchet derivative
ε-Fréchet differentiability
σ-porous sets
Classificazione: SI 830
Altri autori: PreissDavid  
TišerJaroslav <1957->  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and indexes.
Nota di contenuto: Frontmatter -- Contents -- Chapter One: Introduction -- Chapter Two: Gâteaux differentiability of Lipschitz functions -- Chapter Three: Smoothness, convexity, porosity, and separable determination -- Chapter Four: ε-Fréchet differentiability -- Chapter Five: Γ-null and Γn-null sets -- Chapter Six: Férchet differentiability except for Γ-null sets -- Chapter Seven: Variational principles -- Chapter Eight: Smoothness and asymptotic smoothness -- Chapter Nine: Preliminaries to main results -- Chapter Ten: Porosity, Γn- and Γ-null sets -- Chapter Eleven: Porosity and ε-Fréchet differentiability -- Chapter Twelve: Fréchet differentiability of real-valued functions -- Chapter Thirteen: Fréchet differentiability of vector-valued functions -- Chapter Fourteen: Unavoidable porous sets and nondifferentiable maps -- Chapter Fifteen: Asymptotic Fréchet differentiability -- Chapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces -- Bibliography -- Index -- Index of Notation
Sommario/riassunto: 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.
Titolo autorizzato: Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces  Visualizza cluster
ISBN: 1-283-37995-3
9786613379955
1-4008-4269-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910789737103321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: Annals of mathematics studies ; ; no. 179.