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Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces by Mikha

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Item specifics

Condition: Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab

ISBN-13: 9783110263404

Book Title: Metric Embeddings

ISBN: 9783110263404

Subject Area: Mathematics, Computers

Publication Name: Metric Embeddings : Bilipschitz and Coarse Embeddings Into Banach Spaces

Publisher: DE Gruyter Gmbh, Walter

Item Length: 9.4 in

Subject: Functional Analysis, Computer Science, General, Discrete Mathematics

Publication Year: 2013

Series: De Gruyter Studies in Mathematics Ser.

Type: Textbook

Format: Hardcover

Language: English

Author: Mikhail I. Ostrovskii

Item Weight: 27.4 Oz

Item Width: 6.7 in

Number of Pages: 384 Pages

About this product

Product Identifiers

Publisher

DE Gruyter Gmbh, Walter

ISBN-10

3110263408

ISBN-13

9783110263404

eBay Product ID (ePID)

167904768

Product Key Features

Number of Pages

384 Pages

Publication Name

Metric Embeddings : Bilipschitz and Coarse Embeddings Into Banach Spaces

Language

English

Subject

Functional Analysis, Computer Science, General, Discrete Mathematics

Publication Year

2013

Type

Textbook

Subject Area

Mathematics, Computers

Author

Mikhail I. Ostrovskii

Series

De Gruyter Studies in Mathematics Ser.

Format

Hardcover

Dimensions

Item Weight

27.4 Oz

Item Length

9.4 in

Item Width

6.7 in

Additional Product Features

Intended Audience

Scholarly & Professional

Reviews

"Ostrovskii's Metric Embeddings: Bilipchitz and Coarse Embeddings into Banach Spaces is a very valuable addition to the literature. It contains an impressive amount of material and is recommended to anyone having some interest in these geometric problems. The area is developing at an extremely fast pace and it is difficult to find in a book format the recent developments; the monograph under review contains some very interesting ones." Florent B. Baudier and William B. Johnson, Bulletin of the American Mathematical Society "The author has succeeded in making profound material from both the functional analytic and the discrete side accessible to his readers. All the arguments are exposed in great detail, and the line of reasoning is laid out clearly. The book can be highly recommended to researchers who wish to enter the rapidly developing area of metric embeddings." Dirk Werner, Zentralblatt für Mathematik

Grade From

College Graduate Student

Series Volume Number

Illustrated

Yes

Grade To

College Graduate Student

Synopsis

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob., Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include: (1) Embeddability of locally finite metric spaces into Banach spaces is finitely determined; (2) Constructions of embeddings; (3) Distortion in terms of Poincar inequalities; (4) Constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees; (5) Banach spaces which do not admit coarse embeddings of expanders; (6) Structure of metric spaces which are not coarsely embeddable into a Hilbert space; (7) Applications of Markov chains to embeddability problems; (8) Metric characterizations of properties of Banach spaces; (9) Lipschitz free spaces. Substantial part of the book is devoted to a detailed presentation of relevant results of Banach space theory and graph theory. The final chapter contains a list of open problems. Extensive bibliography is also included. Each chapter, except the open problems chapter, contains exercises and a notes and remarks section containing references, discussion of related results, and suggestions for further reading. The book will help readers to enter and to work in a very rapidly developing area having many important connections with different parts of mathematics and computer science., Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include: (1) Embeddability of locally finite metric spaces into Banach spaces is finitely determined; (2) Constructions of embeddings; (3) Distortion in terms of Poincaré inequalities; (4) Constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees; (5) Banach spaces which do not admit coarse embeddings of expanders; (6) Structure of metric spaces which are not coarsely embeddable into a Hilbert space; (7) Applications of Markov chains to embeddability problems; (8) Metric characterizations of properties of Banach spaces; (9) Lipschitz free spaces. Substantial part of the book is devoted to a detailed presentation of relevant results of Banach space theory and graph theory. The final chapter contains a list of open problems. Extensive bibliography is also included. Each chapter, except the open problems chapter, contains exercises and a notes and remarks section containing references, discussion of related results, and suggestions for further reading. The book will help readers to enter and to work in a very rapidly developing area having many important connections with different parts of mathematics and computer science.