skip to content
Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces Preview this item
ClosePreview this item
Checking...

Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces

Author: Joram Lindenstrauss; David Preiss; Jaroslav Tišer
Publisher: Princeton : Princeton University Press, 2012.
Series: Annals of mathematics studies, no. 179.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Joram Lindenstrauss; David Preiss; Jaroslav Tišer
ISBN: 9780691153551 0691153558 9780691153568 0691153566
OCLC Number: 757935618
Description: ix, 425 pages ; 25 cm.
Contents: Gat̂eaux Dfferentiability of Lipschitz Functions --
Smoothness, Convexity, Porosity, and Separable Determination --
e-Frećhet Differentiability --
G-Null and Gn-Null Sets --
Frećhet Differentiability Except for G-Null Sets --
Variational Principles --
Smoothness and Asymptotic Smoothness --
Preliminaries to Main Results --
Porosity, Gn- and G-Null Sets10 --
Porosity and e-Frećhet Differentiability --
Frećhet Differentiability of Real-Valued Functions --
Frećhet Differentiability of Vector-Valued Functions --
Unavoidable Porous Sets and Nondifferentiable Maps --
Asymptotic Frećhet differentiability --
Differentiability of Lipschitz maps on Hilbert spaces.
Series Title: Annals of mathematics studies, no. 179.
Responsibility: Joram Lindenstrauss, David Preiss, Jaroslav Tiser.

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  Read more...

Reviews

Editorial reviews

Publisher Synopsis

"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 Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/757935618> # Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces
    a schema:CreativeWork, schema:Book ;
    library:oclcnum "757935618" ;
    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/lipschitz_bedingung> ; # Lipschitz-Bedingung
    schema:about <http://id.worldcat.org/fast/935782> ; # Fréchet spaces
    schema:about <http://id.worldcat.org/fast/936061> ; # Functional analysis
    schema:about <http://experiment.worldcat.org/entity/work/data/1029425488#Topic/frechet_differenzierbarkeit> ; # Fréchet-Differenzierbarkeit
    schema:about <http://dewey.info/class/515.88/e23/> ;
    schema:about <http://id.worldcat.org/fast/826389> ; # Banach spaces
    schema:about <http://id.worldcat.org/fast/999438> ; # Lipschitz spaces
    schema:about <http://id.worldcat.org/fast/844140> ; # Calculus of variations
    schema:bookFormat bgn:PrintBook ;
    schema:contributor <http://viaf.org/viaf/84902071> ; # Jaroslav Tišer
    schema:contributor <http://viaf.org/viaf/78600431> ; # David Preiss
    schema:creator <http://viaf.org/viaf/22221499> ; # Joram Lindenstrauss
    schema:datePublished "2012" ;
    schema:description "Gat̂eaux Dfferentiability of Lipschitz Functions -- Smoothness, Convexity, Porosity, and Separable Determination -- e-Frećhet Differentiability -- G-Null and Gn-Null Sets -- Frećhet Differentiability Except for G-Null Sets -- Variational Principles -- Smoothness and Asymptotic Smoothness -- Preliminaries to Main Results -- Porosity, Gn- and G-Null Sets10 -- Porosity and e-Frećhet Differentiability -- Frećhet Differentiability of Real-Valued Functions -- Frećhet Differentiability of Vector-Valued Functions -- Unavoidable Porous Sets and Nondifferentiable Maps -- Asymptotic Frećhet differentiability -- Differentiability of Lipschitz maps on Hilbert spaces."@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:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/1029425488#Series/annals_of_mathematics_studies> ; # Annals of mathematics studies ;
    schema:name "Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces"@en ;
    schema:productID "757935618" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/757935618#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://site.ebrary.com/id/10521870> ;
    schema:workExample <http://worldcat.org/isbn/9780691153551> ;
    schema:workExample <http://worldcat.org/isbn/9780691153568> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/757935618> ;
    .


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/757935618> ; # Fréchet 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/frechet_differenzierbarkeit> # Fréchet-Differenzierbarkeit
    a schema:Intangible ;
    schema:name "Fréchet-Differenzierbarkeit"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1029425488#Topic/lipschitz_bedingung> # Lipschitz-Bedingung
    a schema:Intangible ;
    schema:name "Lipschitz-Bedingung"@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/935782> # Fréchet spaces
    a schema:Intangible ;
    schema:name "Fréchet spaces"@en ;
    .

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

<http://id.worldcat.org/fast/999438> # Lipschitz spaces
    a schema:Intangible ;
    schema:name "Lipschitz spaces"@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/78600431> # 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/isbn/9780691153551>
    a schema:ProductModel ;
    schema:isbn "0691153558" ;
    schema:isbn "9780691153551" ;
    .

<http://worldcat.org/isbn/9780691153568>
    a schema:ProductModel ;
    schema:isbn "0691153566" ;
    schema:isbn "9780691153568" ;
    .

<http://www.worldcat.org/title/-/oclc/757935618>
    a genont:InformationResource, genont:ContentTypeGenericResource ;
    schema:about <http://www.worldcat.org/oclc/757935618> ; # Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces
    schema:dateModified "2017-11-29" ;
    void:inDataset <http://purl.oclc.org/dataset/WorldCat> ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.