Lipschitz Functions
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Beschreibung
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.
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.
Winner of the 2019 Prize DIMITRIE POMPEIU of the Romanian Academy Full treatment of basic properties of Lipschitz functions with numerous examples A thorough presentation of various extension results for (scalar and vector) Lipschitz functions Full treatment of Banach spaces of Lipschitz functions and of operators acting on them A presentation of Lipschitz free Banach spaces with applications to Kantorovich duality in the mass transportation problem
Autor*in
Ştefan Cobzaş
Themen in »Lipschitz Functions«
Banach Spaces of Lipschitz Functions Bishop-Phelps Property Compact Operators Composition Operators Extension Properties for Lipschitz Operators Geodesic Metric Spaces Holder Functions Lipschitz Free Banach Spaces Lipschitz Functions Lipschitz Operators Metric Spaces Nonlinear Embeddings
Stimmen zu »Lipschitz Functions«
"This is an excellent source for all aspects of the notion of Lipschitz continuity and will undoubtedly become a standard reference.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 196 (1), 2021)
“The book is accessible to graduate students, but it also contains recent results of interest to researchers in various domains as metric geometry, mathematical analysis, and functional analysis. My opinion this book will be of interest to everyone whose domain of interest is mathematical analysis and its applications.” (Andrey Zahariev, zbMATH 1431.26002, 2020)“This book provides a very large amount of interesting information. … it is very useful that they are brought to readers' attention.” (Mikhail Ostrovskii, Mathematical Reviews, December, 2019)
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