Lipschitz Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lipschitz Functions write by Ştefan Cobzaş. This book was released on 2019-05-23. Lipschitz Functions available in PDF, EPUB and Kindle. 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.
Lipschitz Functions
Lipschitz Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lipschitz Functions write by Ştefan Cobzaş. This book was released on 2019-05-23. Lipschitz Functions available in PDF, EPUB and Kindle. 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.
Lipschitz Algebras
Lipschitz Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lipschitz Algebras write by Nik Weaver. This book was released on 1999. Lipschitz Algebras available in PDF, EPUB and Kindle. The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces write by Joram Lindenstrauss. This book was released on 2012-02-26. Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces available in PDF, EPUB and Kindle. 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.
Basic Real Analysis
Basic Real Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Basic Real Analysis write by Houshang H. Sohrab. This book was released on 2003-06-03. Basic Real Analysis available in PDF, EPUB and Kindle. Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.
