UID:
almafu_9958354083102883
Format:
1 online resource(xii,372p.) :
,
illustrations.
Edition:
Electronic reproduction. Berlin/Boston : De Gruyter, 2013. Mode of access: World Wide Web.
Edition:
System requirements: Web browser.
Edition:
Access may be restricted to users at subscribing institutions.
ISBN:
9783110264012
Series Statement:
De Gruyter Studies in Mathematics; 49
Content:
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. 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 embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poincaré inequalities, constructions of families of expanders and of families of graphs with unbounded girth and lower bounds on average degrees, Banach spaces which do not admit coarse embeddings of expanders, structure of metric spaces which are not coarsely embeddable into a Hilbert space, applications of Markov chains to embeddability problem, metric characterizations of properties of Banach spaces, and Lipschitz free spaces.
Note:
Frontmatter --
,
Preface --
,
Contents --
,
Chapter 1. Introduction: examples of metrics, embeddings, and applications --
,
Chapter 2. Embeddability of locally finite metric spaces into Banach spaces is finitely determined. Related Banach space theory --
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Chapter 3. Constructions of embeddings --
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Chapter 4. Obstacles for embeddability: Poincaré inequalities --
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Chapter 5. Families of expanders and of graphs with large girth --
,
Chapter 6. Banach spaces which do not admit uniformly coarse embeddings of expanders --
,
Chapter 7. Structure properties of spaces which are not coarsely embeddable into a Hilbert space --
,
Chapter 8. Applications of Markov chains to embeddability problems --
,
Chapter 9. Metric characterizations of classes of Banach spaces --
,
Chapter 10. Lipschitz free spaces --
,
Chapter 11. Open problems --
,
Bibliography --
,
Author index --
,
Subject index.
,
Also available in print edition.
,
In English.
Additional Edition:
ISBN 9783110263404
Additional Edition:
ISBN 9783119166225
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9783110264012
URL:
https://doi.org/10.1515/9783110264012
URL:
Volltext
(URL des Erstveröffentlichers)
URL:
Volltext
(lizenzpflichtig)
URL:
https://doi.org/10.1515/9783110264012
URL:
https://www.degruyter.com/isbn/9783110264012
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