Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (Am-179) (Annals of Mathematics Studies #179) (Paperback)

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (Am-179) (Annals of Mathematics Studies #179) By Joram Lindenstrauss, David Preiss, Jaroslav Tiser Cover Image

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (Am-179) (Annals of Mathematics Studies #179) (Paperback)

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This book makes a significant inroad into the unexpectedly difficult question of existence of Fr chet 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 Fr chet 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 Fr chet 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.
Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Tišer is associate professor of mathematics at Czech Technical University in Prague.
Product Details ISBN: 9780691153568
ISBN-10: 0691153566
Publisher: Princeton University Press
Publication Date: February 26th, 2012
Pages: 440
Language: English
Series: Annals of Mathematics Studies