Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces
 Responsibility
 Joram Lindenstrauss, David Preiss, Jaroslav Tiser.
 Language
 English.
 Imprint
 Princeton : Princeton University Press, 2012.
 Physical description
 ix, 425 p. ; 25 cm.
 Series
 Annals of mathematics studies ; no. 179.
Access
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Math & Statistics Library

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QA1 .A665 NO.179

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QA1 .A665 NO.179
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Creators/Contributors
 Author/Creator
 Lindenstrauss, Joram, 19362012
 Contributor
 Preiss, David.
 Tišer, Jaroslav, 1957
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [415]418) and indexes.
 Publisher's Summary
 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 vectorvalued 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 vectorvalued 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.
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Subjects
Bibliographic information
 Publication date
 2012
 Series
 Annals of mathematics studies ; no. 179
 ISBN
 9780691153551 (hardcover)
 0691153558 (hardcover)
 9780691153568 (pbk.)
 0691153566 (pbk.)