Mathematics
Ebook Central Academic Complete
9781400842698
1400842697
Banach spaces
Lipschitz spaces
ProQuest Ebook Central
nju
(Unlimited Concurrent Users)
from Ebook Central Academic Complete
2017-07-27
Annals of mathematics studies ;
(Unlimited Concurrent Users)
from Ebook Central Academic Complete
(Unlimited Concurrent Users)
from Ebook Central Academic Complete
769343169
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces.
Electronic books
2012
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
769343169
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.
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MATHEMATICS--Calculus
Lindenstrauss
Joram
Joram Lindenstrauss
1936
2012
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces.
Print version:
(Unlimited Concurrent Users)
from EBSCO Academic Collection
Preiss
David
David Preiss
MATHEMATICS--Mathematical Analysis
Calculus of variations
9781283379953
1283379953
Functional analysis
Princeton University Press
2012
Princeton
MATHEMATICS--Set Theory
Fréchet spaces
Tišer
Jaroslav
Jaroslav Tišer
1957
Moravian eBooks
(Unlimited Concurrent Users)
from Ebook Central Academic Complete