Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (BOK)

Joram Lindenstrauss, David Preiss, Jaroslav Tiser

529,00 52900
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This book makes a significant inroad into the unexpectedly difficult question of existence of Frchet 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 Frchet 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 Frchet 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.

Produktfakta

Språk Engelsk Engelsk Innbinding Heftet
Utgitt 2012 Forfatter David Preiss, Jaroslav Tiser, Joram Lindenstrauss
Forlag
University Press Group Ltd
ISBN 9780691153568
Antall sider 440 Dimensjoner 15,2cm x 22,9cm x 2,5cm
Vekt 628 gram Leverandør Bertram Trading Ltd
Emner og form Functional analysis & transforms