About this 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.
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
- DOI https://doi.org/10.1007/978-3-030-16489-8
- Copyright Information Springer Nature Switzerland AG 2019
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-030-16488-1
- Online ISBN 978-3-030-16489-8
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
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- Finance, Business & Banking