Geometric Nonlinear Functional Analysis
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Geometric Nonlinear Functional Analysis
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Author : Yoav Benyamini
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Geometric Nonlinear Functional Analysis written by Yoav Benyamini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories. Many recent rather deep theorems and delicate examples are included with complete and detailed proofs. Challenging open problems are described and explained, and promising new research directions are indicated.
Geometric Nonlinear Functional Analysis
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Author : Yoav Benyamini
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Geometric Nonlinear Functional Analysis written by Yoav Benyamini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.
Geometric Nonlinear Functional Analysis
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Author : Yoav Benyamini
language : en
Publisher: Amer Mathematical Society
Release Date : 2000
Geometric Nonlinear Functional Analysis written by Yoav Benyamini and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories. Many recent rather deep theorems and delicate examples are included with complete and detailed proofs. Challenging open problems are described and explained, and promising new research directions are indicated.
Geometric Nonlinear Functional Analysis
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Author : Yoav Benyamini
language : en
Publisher:
Release Date : 1999
Geometric Nonlinear Functional Analysis written by Yoav Benyamini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Nonlinear functional analysis categories.
The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (e.g., differentiability, stability, approximation, existence of extensions, fixed points, etc.). This study leads naturally also to the classification of.
Geometric Nonlinear Functional Analysis
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Author : Yoav Benyamini
language : en
Publisher:
Release Date : 1927
Geometric Nonlinear Functional Analysis written by Yoav Benyamini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.
Topics In Nonlinear Functional Analysis
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Author : L. Nirenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
Topics In Nonlinear Functional Analysis written by L. Nirenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems. For more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Nigel Kalton S Lectures In Nonlinear Functional Analysis
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Author : Adam Bowers
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-02
Nigel Kalton S Lectures In Nonlinear Functional Analysis written by Adam Bowers and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-02 with Mathematics categories.
The main theme of the book is the nonlinear geometry of Banach spaces, and it considers various significant problems in the field. The present book is a commented transcript of the notes of the graduate-level topics course in nonlinear functional analysis given by the late Nigel Kalton in 2008. Nonlinear geometry of Banach spaces is a very active area of research with connections to theoretical computer science, noncommutative geometry, as well as geometric group theory. Nigel Kalton was the most influential and prolific contributor to the theory. Collected here are the topics that Nigel Kalton felt were significant for those first dipping a toe into the subject of nonlinear functional analysis and presents these topics in an accessible and concise manner. As well as covering some well-known topics, it also includes recent results discovered by Kalton and his collaborators which have not previously appeared in textbook form. A typical first-year course in functional analysis will provide sufficient background for readers of this book.
Functional Analysis And Infinite Dimensional Geometry
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Author : Marián J. Fabian
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-25
Functional Analysis And Infinite Dimensional Geometry written by Marián J. Fabian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-25 with Mathematics categories.
This book introduces the reader to the basic principles of functional analysis and to areas of Banach space theory that are close to nonlinear analysis and topology. In the first part, the book develops the classical theory, including weak topologies, locally convex spaces, Schauder bases, and compact operator theory. The presentation is self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology. The second part covers topics in convexity and smoothness, finite representability, variational principles, homeomorphisms, weak compactness and more. Several results are published here for the first time in a monograph. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints. The book is also directed to young researchers in functional analysis and can serve as a reference book.This is an introduction to basic principles of functional analysis and to areas of Banach space theory close to nonlinear analysis and topology. The first part, which develops the classical theory, is self-contained and features a large number of exercises containing many important results. The second part covers selected topics in the theory of Banach spaces related to smoothness and topology. It is intended to be an introduction to and complement of existing books on the subject. This text may be used in graduate courses, for independent study, or as a reference book.
Convex Analysis And Nonlinear Geometric Elliptic Equations
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Author : Ilya J. Bakelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Convex Analysis And Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
Nonlinear Analysis Geometry And Applications
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Author : Diaraf Seck
language : en
Publisher: Birkhäuser
Release Date : 2020-11-21
Nonlinear Analysis Geometry And Applications written by Diaraf Seck and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.