Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Joram Lindenstrauss

ISBN 10: 0691153566 / ISBN 13: 9780691153568

Published by Princeton University Press, 2012

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 the classical topic of existence of derivatives of vector-valued Lipschitz functions. Series: Annals of Mathematics Studies. Num Pages: 440 pages. BIC Classification: PBKF. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 233 x 164 x 22. Weight in Grams: 616. . 2012. Paperback. . . . . Books ship from the US and Ireland. Seller Inventory # V9780691153568

Synopsis:

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.

About the Author: 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.

Bibliographic Details

Title: Fréchet Differentiability of Lipschitz ...
Publisher: Princeton University Press
Publication Date: 2012
Binding: Soft cover
Condition: New