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Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

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Title: Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Description: 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.
Authors: Joram Lindenstrauss, David Preiss, Jaroslav Tišer
Resource Type: eBook.
Subjects: Functional analysis, Calculus of variations, Banach spaces
Categories: MATHEMATICS / Calculus, MATHEMATICS / Game Theory, MATHEMATICS / Set Theory, MATHEMATICS / Vector Analysis, MATHEMATICS / Functional Analysis
Database: eBook Collection (EBSCOhost)
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 421487
RelevancyScore: 1044
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1044.26904296875
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  Data: Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
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  Label: Description
  Group: Ab
  Data: 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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  Data: <searchLink fieldCode="AR" term="%22Joram+Lindenstrauss%22">Joram Lindenstrauss</searchLink><br /><searchLink fieldCode="AR" term="%22David+Preiss%22">David Preiss</searchLink><br /><searchLink fieldCode="AR" term="%22Jaroslav+Tišer%22">Jaroslav Tišer</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br /><searchLink fieldCode="DE" term="%22Banach+spaces%22">Banach spaces</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.88
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Functional analysis
        Type: general
      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Banach spaces
        Type: general
    Titles:
      – TitleFull: Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Joram Lindenstrauss
      – PersonEntity:
          Name:
            NameFull: David Preiss
      – PersonEntity:
          Name:
            NameFull: Jaroslav Tišer
      – PersonEntity:
          Name:
            NameFull: Joram Lindenstrauss
      – PersonEntity:
          Name:
            NameFull: David Preiss
      – PersonEntity:
          Name:
            NameFull: Jaroslav Tišer
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2012
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780691153568
            – Type: isbn-print
              Value: 9780691153551
            – Type: isbn-electronic
              Value: 9781400842698
          Titles:
            – TitleFull: Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
              Type: main
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