Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Joram Lindenstrauss, David Preiss, Jaroslav Tiser

ISBN 10: 0691153558 / ISBN 13: 9780691153551

Verlag: Princeton University Press, US, 2012

Beschreibung

This book makes a significant inroad into the unexpectedly difficult question of existence of Frechet 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 Frechet 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 Frechet 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.

Bestandsnummer des Verkäufers LU-9780691153551

Bibliografische Details

• Titel: Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
• Verlag: Princeton University Press, US
• Erscheinungsjahr: 2012
• Sprache: Englisch
• ISBN-10: 0691153558
• ISBN-13: 9780691153551
• Einband: Hardback
• Zustand: New
• Gewicht: 482 Gramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

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 Tier is associate professor of mathematics at Czech Technical University in Prague.