Lipschitz Functions

✍ Scribed by Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 605
• Series: Lecture Notes in Mathematics 2241
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xiv
Prerequisites (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 1-97
Basic Facts Concerning Lipschitz Functions (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 99-142
Relations with Other Classes of Functions (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 143-210
Extension Results for Lipschitz Mappings (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 211-251
Extension Results for Lipschitz Mappings in Geodesic Spaces (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 253-316
Approximations Involving Lipschitz Functions (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 317-334
Lipschitz Isomorphisms of Metric Spaces (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 335-363
Banach Spaces of Lipschitz Functions (Ştefan Cobzaş, Radu Miculescu, Adriana Nicolae)....Pages 365-556
Back Matter ....Pages 557-593

✦ Subjects

Mathematics; Functional Analysis; Real Functions; Approximations and Expansions; Operator Theory; Convex and Discrete Geometry