Frechet Differentiability Of Lipschitz Functions And Porous Sets In Banach Spaces

Author : Joram Lindenstrauss
Publisher : Princeton University Press
ISBN 13 : 1400842697
Total Pages : 436 pages
Book Rating : 4.98/5 ( download)

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Download or read book Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces written by Joram Lindenstrauss and published by Princeton University Press. This book was released on 2012-02-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Joram Lindenstrauss
Publisher : Princeton University Press
ISBN 13 : 0691153566
Total Pages : 440 pages
Book Rating : 4.68/5 ( download)

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Download or read book Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces written by Joram Lindenstrauss and published by Princeton University Press. This book was released on 2012-02-26 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Joram Lindenstrauss
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3Q/5 ( download)

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Download or read book Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces written by Joram Lindenstrauss and published by . This book was released on 1940 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ştefan Cobzaş
Publisher : Springer
ISBN 13 : 3030164896
Total Pages : 605 pages
Book Rating : 4.98/5 ( download)

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Download or read book Lipschitz Functions written by Ştefan Cobzaş and published by Springer. This book was released on 2019-05-23 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.

Author : Antonio J. Guirao
Publisher : Springer
ISBN 13 : 3319335723
Total Pages : 179 pages
Book Rating : 4.28/5 ( download)

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Download or read book Open Problems in the Geometry and Analysis of Banach Spaces written by Antonio J. Guirao and published by Springer. This book was released on 2016-07-26 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.

Author : K.D. Bierstedt
Publisher : Elsevier
ISBN 13 : 0080515924
Total Pages : 469 pages
Book Rating : 4.22/5 ( download)

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Download or read book Recent Progress in Functional Analysis written by K.D. Bierstedt and published by Elsevier. This book was released on 2001-09-20 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.

Author : Petr Hájek
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110258994
Total Pages : 514 pages
Book Rating : 4.98/5 ( download)

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Download or read book Smooth Analysis in Banach Spaces written by Petr Hájek and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-29 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.

Author : Rajendra Bhatia
Publisher : World Scientific
ISBN 13 : 9814462934
Total Pages : 4137 pages
Book Rating : 4.38/5 ( download)

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Download or read book Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1001 pages
Book Rating : 4./5 ( download)

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Download or read book written by and published by World Scientific. This book was released on with total page 1001 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Beata Randrianantoanina
Publisher : Walter de Gruyter
ISBN 13 : 3110918293
Total Pages : 465 pages
Book Rating : 4.98/5 ( download)

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Download or read book Banach Spaces and their Applications in Analysis written by Beata Randrianantoanina and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.