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  2. Regning og matematisk analyse
  3. Funktionsanalyse og transformation

Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Af: Joram Lindenstrauss, David Preiss, Jaroslav Tiser Engelsk Paperback

Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Af: Joram Lindenstrauss, David Preiss, Jaroslav Tiser Engelsk Paperback
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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.

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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.

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Produktdetaljer
Sprog: Engelsk
Sider: 464
ISBN-13: 9780691153568
Indbinding: Paperback
Udgave:
ISBN-10: 0691153566
Kategori: Funktionsanalyse og transformation
Udg. Dato: 26 feb 2012
Længde: 22mm
Bredde: 164mm
Højde: 233mm
Forlag: Princeton University Press
Oplagsdato: 26 feb 2012
Forfatter(e): Joram Lindenstrauss, David Preiss, Jaroslav Tiser
Forfatter(e) Joram Lindenstrauss, David Preiss, Jaroslav Tiser

Kategori Funktionsanalyse og transformation

ISBN-13 9780691153568

Sprog Engelsk

Indbinding Paperback

Sider 464

Udgave

Længde 22mm

Bredde 164mm

Højde 233mm

Udg. Dato 26 feb 2012

Oplagsdato 26 feb 2012

Forlag Princeton University Press

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