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  • 1
    UID:
    almahu_9949462112702882
    Format: 1 online resource (372 p.)
    ISBN: 9783110264012 , 9783110494938
    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 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.
    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 -- , Chapter 3. Constructions of embeddings -- , Chapter 4. Obstacles for embeddability: Poincaré inequalities -- , 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 , Issued also in print. , Mode of access: Internet via World Wide Web. , In English.
    In: DG Studies in Mathematics eBook-Package, De Gruyter, 9783110494938
    In: DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
    In: DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
    In: DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
    In: E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013, De Gruyter, 9783110317350
    In: E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013, De Gruyter, 9783110317282
    In: E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013, De Gruyter, 9783110317275
    Additional Edition: ISBN 9783110263404
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Electronic books
    URL: Cover
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Cover
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    UID:
    almahu_BV041105555
    Format: XI, 372 S. ; , 240 mm x 170 mm.
    ISBN: 3-11-026340-8 , 978-3-11-026340-4 , 978-3-11-916622-5
    Series Statement: De Gruyter Studies in Mathematics 49
    Note: Literaturverz. S. [335] - 360
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-11-026401-2
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Einbettung ; Diskreter metrischer Raum ; Banach-Raum
    Author information: Ostrovskii, Mikhail I.
    Library Location Call Number Volume/Issue/Year Availability
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  • 3
    Book
    Book
    Berlin [u.a.] : Walter de Gruyter & Co.
    UID:
    kobvindex_ZLB15680010
    Format: XI, 372 Seiten
    ISBN: 978-3-11-026340-4 , 3-11-026340-8
    Series Statement: De Gruyter studies in mathematics 49
    Note: Literaturangaben
    Language: English
    Author information: Ostrovskii, Mikhail I.
    Library Location Call Number Volume/Issue/Year Availability
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  • 4
    UID:
    almatuudk_9922633130802884
    Format: 1 online resource (384 p.)
    Edition: 1st ed.
    ISBN: 9783110263404 , 3110263408
    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 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.
    Note: Description based upon print version of record. , Front matter -- , 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 -- , Chapter 3. Constructions of embeddings -- , Chapter 4. Obstacles for embeddability: Poincaré inequalities -- , 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 , Issued also in print. , English
    Additional Edition: ISBN 9783110264012
    Additional Edition: ISBN 3110264013
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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  • 5
    UID:
    almahu_9948318001902882
    Format: 1 online resource (384 pages)
    ISBN: 9783110264012 (e-book)
    Series Statement: De Gruyter studies in mathematics
    Language: English
    Keywords: Electronic books.
    Library Location Call Number Volume/Issue/Year Availability
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