zum Inhalt wechseln
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces Titelvorschau
SchließenTitelvorschau
Prüfung…

Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Verfasser/in: Joram Lindenstrauss; David Preiss; Jaroslav Tišer
Verlag: Princeton : Princeton University Press, 2012.
Serien: Annals of mathematics studies, no. 179.
Ausgabe/Format   E-Book : Dokument : EnglischAlle Ausgaben und Formate anzeigen
Datenbank:WorldCat
Zusammenfassung:
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  Weiterlesen…
Bewertung:

(noch nicht bewertet) 0 mit Rezensionen - Verfassen Sie als Erste eine Rezension.

Themen
Ähnliche Titel

 

Exemplar ausleihen

&AllPage.SpinnerRetrieving; Suche nach Bibliotheken, die diesen Titel besitzen ...

Details

Gattung/Form: Electronic books
Physisches Format Print version:
Lindenstrauss, Joram.
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces.
Princeton : Princeton University Press, ©2012
Medientyp: Dokument, Internetquelle
Dokumenttyp: Internet-Ressource, Computer-Datei
Alle Autoren: Joram Lindenstrauss; David Preiss; Jaroslav Tišer
ISBN: 9781400842698 1400842697 1283379953 9781283379953
OCLC-Nummer: 769343169
Anmerkungen: 14.7 Proof of Theorem.
Beschreibung: 1 online resource (436 pages).
Inhalt: Cover; Title Page; Copyright Page; Table of Contents; Chapter 1. Introduction; 1.1 Key notions and notation; Chapter 2. Gâteaux Dfferentiability of Lipschitz Functions; 2.1 Radon-Nikodým Property; 2.2 Haar and Aronszajn-Gauss Null Sets; 2.3 Existence Results for Gâteaux Derivatives; 2.4 Mean Value Estimates; Chapter 3. Smoothness, Convexity, Porosity, and Separable Determination; 3.1 A criterion of Differentiability of Convex Functions; 3.2 Fréchet Smooth and Nonsmooth Renormings; 3.3 Fréchet Differentiability of Convex Functions; 3.4 Porosity and Nondifferentiability. 3.5 Sets of Fréchet Differentiability Points3.6 Separable Determination; Chapter 4. e-Fréchet Differentiability; 4.1 e-Differentiability and Uniform Smoothness; 4.2 Asymptotic Uniform Smoothness; 4.3 e-Fréchet Differentiability of Functions on Asymptotically Smooth Spaces; Chapter 5. G-Null and Gn-Null Sets; 5.1 Introduction; 5.2 G-Null Sets and Gâteaux Differentiability; 5.3 Spaces of Surfaces; 5.4 G- and Gn-Null Sets of low Borel Classes; 5.5 Equivalent Definitions of Gn-Null Sets; 5.6 Separable Determination; Chapter 6. Fréchet Differentiability Except for G-Null Sets; 6.1 Introduction. 6.2 Regular Points6.3 A Criterion of Fréchet Differentiability; 6.4 Fréchet Differentiability Except for G-Null Sets; Chapter 7. Variational Principles; 7.1 Introduction; 7.2 Variational Principles via Games; 7.3 Bimetric Variational Principles; Chapter 8. Smoothness and Asymptotic Smoothness; 8.1 Modulus of Smoothness; 8.2 Smooth Bumps with Controlled Modulus; Chapter 9. Preliminaries to Main Results; 9.1 Notation, Linear Operators, Tensor Products; 9.2 Derivatives and Regularity; 9.3 Deformation of Surfaces Controlled by?n; 9.4 Divergence Theorem; 9.5 Some Integral Estimates. Chapter 10. Porosity, Gn- and G-Null Sets10.1 Porous and s-Porous Sets; 10.2 A Criterion of Gn-nullness of Porous Sets; 10.3 Directional Porosity and Gn-Nullness; 10.4 s-Porosity and Gn-Nullness; 10.5 G1-Nullness of Porous Sets and Asplundness; 10.6 Spaces in which s-Porous Sets are G-Null; Chapter 11. Porosity and e-Fréchet Differentiability; 11.1 Introduction; 11.2 Finite Dimensional Approximation; 11.3 Slices and e-Differentiability; Chapter 12. Fréchet Differentiability of Real-Valued Functions; 12.1 Introduction and Main Results; 12.2 An Illustrative Special Case. 12.3 A Mean Value Estimate12.4 Proof of Theorems; 12.5 Generalizations and Extensions; Chapter 13. Fréchet Differentiability of Vector-Valued Functions; 13.1 Main Results; 13.2 Regularity Parameter; 13.3 Reduction to a Special Case; 13.4 Regular Fréchet Differentiability; 13.5 Fréchet Differentiability; 13.6 Simpler Special Cases; Chapter 14. Unavoidable Porous Sets and Nondifferentiable Maps; 14.1 Introduction and Main Results; 14.2 An Unavoidable Porous Set in l1; 14.3 Preliminaries to Proofs of Main Results; 14.4 The Main Construction; 14.5 The Main Construction; 14.6 Proof of Theorem.
Serientitel: Annals of mathematics studies, no. 179.

Abstract:

Focuses on the difficult question of existence of Frchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. This book provides a bridge between descriptive set theory and  Weiterlesen…

Rezensionen

Redaktionelle Rezension

Nielsen BookData

"The book is well written--as one would expect from its distinguished authors, including the late Joram Lindestrauss (1936-2012). It contains many fascinating and profound results. It no doubt will Weiterlesen…

 
Nutzer-Rezensionen
Suche nach GoodReads-Rezensionen
Suche nach DOGObooks-Rezensionen…

Tags

Tragen Sie als Erste Tags ein.

Ähnliche Titel

Anfrage bestätigen

Sie haben diesen Titel bereits angefordert. Wenn Sie trotzdem fortfahren möchten, klicken Sie auf OK.

Verlinkung


Primary Entity

<http://www.worldcat.org/oclc/769343169> # Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
    a schema:Book, schema:CreativeWork, schema:MediaObject ;
    library:oclcnum "769343169" ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/1029425488#Place/princeton> ; # Princeton
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nju> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics_mathematical_analysis> ; # MATHEMATICS--Mathematical Analysis
    schema:about <http://id.worldcat.org/fast/826389> ; # Banach spaces
    schema:about <http://dewey.info/class/515.88/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/lipschitz_spaces> ; # Lipschitz spaces
    schema:about <http://id.worldcat.org/fast/844140> ; # Calculus of variations
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics_set_theory> ; # MATHEMATICS--Set Theory
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics> ; # Mathematics
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/frechet_spaces> ; # Fréchet spaces
    schema:about <http://id.worldcat.org/fast/936061> ; # Functional analysis
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics_calculus> ; # MATHEMATICS--Calculus
    schema:bookFormat schema:EBook ;
    schema:contributor <http://viaf.org/viaf/73444643> ; # David Preiss
    schema:contributor <http://viaf.org/viaf/84902071> ; # Jaroslav Tišer
    schema:creator <http://viaf.org/viaf/22221499> ; # Joram Lindenstrauss
    schema:datePublished "2012" ;
    schema:description "Cover; Title Page; Copyright Page; Table of Contents; Chapter 1. Introduction; 1.1 Key notions and notation; Chapter 2. Gâteaux Dfferentiability of Lipschitz Functions; 2.1 Radon-Nikodým Property; 2.2 Haar and Aronszajn-Gauss Null Sets; 2.3 Existence Results for Gâteaux Derivatives; 2.4 Mean Value Estimates; Chapter 3. Smoothness, Convexity, Porosity, and Separable Determination; 3.1 A criterion of Differentiability of Convex Functions; 3.2 Fréchet Smooth and Nonsmooth Renormings; 3.3 Fréchet Differentiability of Convex Functions; 3.4 Porosity and Nondifferentiability."@en ;
    schema: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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/1029425488> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/1029425488#Series/annals_of_mathematics_studies> ; # Annals of mathematics studies ;
    schema:isSimilarTo <http://worldcat.org/entity/work/data/1029425488#CreativeWork/frechet_differentiability_of_lipschitz_functions_and_porous_sets_in_banach_spaces> ;
    schema:name "Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces"@en ;
    schema:productID "769343169" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/769343169#PublicationEvent/princeton_princeton_university_press_2012> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/1029425488#Agent/princeton_university_press> ; # Princeton University Press
    schema:url <http://www.myilibrary.com?id=337995> ;
    schema:url <http://proquest.tech.safaribooksonline.de/9780691153568> ;
    schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=827806> ;
    schema:url <http://www.jstor.org/stable/10.2307/j.ctt7svpc> ;
    schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=421487> ;
    schema:url <http://proquest.safaribooksonline.com/9780691153568> ;
    schema:url <http://site.ebrary.com/id/10521870> ;
    schema:url <http://www.myilibrary.com?id=337995&ref=toc> ;
    schema:url <http://swb.eblib.com/patron/FullRecord.aspx?p=827806> ;
    schema:url <http://proquest.safaribooksonline.com/?fpi=9780691153568> ;
    schema:workExample <http://worldcat.org/isbn/9781283379953> ;
    schema:workExample <http://worldcat.org/isbn/9781400842698> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/769343169> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/1029425488#Agent/princeton_university_press> # Princeton University Press
    a bgn:Agent ;
    schema:name "Princeton University Press" ;
    .

<http://experiment.worldcat.org/entity/work/data/1029425488#Series/annals_of_mathematics_studies> # Annals of mathematics studies ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/769343169> ; # Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
    schema:name "Annals of mathematics studies ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics_calculus> # MATHEMATICS--Calculus
    a schema:Intangible ;
    schema:name "MATHEMATICS--Calculus"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics_mathematical_analysis> # MATHEMATICS--Mathematical Analysis
    a schema:Intangible ;
    schema:name "MATHEMATICS--Mathematical Analysis"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1029425488#Topic/mathematics_set_theory> # MATHEMATICS--Set Theory
    a schema:Intangible ;
    schema:name "MATHEMATICS--Set Theory"@en ;
    .

<http://id.worldcat.org/fast/826389> # Banach spaces
    a schema:Intangible ;
    schema:name "Banach spaces"@en ;
    .

<http://id.worldcat.org/fast/844140> # Calculus of variations
    a schema:Intangible ;
    schema:name "Calculus of variations"@en ;
    .

<http://id.worldcat.org/fast/936061> # Functional analysis
    a schema:Intangible ;
    schema:name "Functional analysis"@en ;
    .

<http://viaf.org/viaf/22221499> # Joram Lindenstrauss
    a schema:Person ;
    schema:birthDate "1936" ;
    schema:deathDate "2012" ;
    schema:familyName "Lindenstrauss" ;
    schema:givenName "Joram" ;
    schema:name "Joram Lindenstrauss" ;
    .

<http://viaf.org/viaf/73444643> # David Preiss
    a schema:Person ;
    schema:familyName "Preiss" ;
    schema:givenName "David" ;
    schema:name "David Preiss" ;
    .

<http://viaf.org/viaf/84902071> # Jaroslav Tišer
    a schema:Person ;
    schema:birthDate "1957" ;
    schema:familyName "Tišer" ;
    schema:givenName "Jaroslav" ;
    schema:name "Jaroslav Tišer" ;
    .

<http://worldcat.org/entity/work/data/1029425488#CreativeWork/frechet_differentiability_of_lipschitz_functions_and_porous_sets_in_banach_spaces>
    a schema:CreativeWork ;
    rdfs:label "Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/769343169> ; # Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
    .

<http://worldcat.org/isbn/9781283379953>
    a schema:ProductModel ;
    schema:isbn "1283379953" ;
    schema:isbn "9781283379953" ;
    .

<http://worldcat.org/isbn/9781400842698>
    a schema:ProductModel ;
    schema:description "electronic bk." ;
    schema:isbn "1400842697" ;
    schema:isbn "9781400842698" ;
    .

<http://www.worldcat.org/title/-/oclc/769343169>
    a genont:InformationResource, genont:ContentTypeGenericResource ;
    schema:about <http://www.worldcat.org/oclc/769343169> ; # Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
    schema:dateModified "2015-06-12" ;
    void:inDataset <http://purl.oclc.org/dataset/WorldCat> ;
    .


Content-negotiable representations

Fenster schließen

Bitte in WorldCat einloggen 

Sie haben kein Konto? Sie können sehr einfach ein kostenloses Konto anlegen,.