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  • 1
    Online-Ressource
    Online-Ressource
    Berlin/Boston :De Gruyter,
    UID:
    almafu_9958354083102883
    Umfang: 1 online resource(xii,372p.) : , illustrations.
    Ausgabe: Electronic reproduction. Berlin/Boston : De Gruyter, 2013. Mode of access: World Wide Web.
    Ausgabe: System requirements: Web browser.
    Ausgabe: Access may be restricted to users at subscribing institutions.
    ISBN: 9783110264012
    Serie: De Gruyter Studies in Mathematics; 49
    Inhalt: 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.
    Anmerkung: 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. , Also available in print edition. , In English.
    Weitere Ausg.: ISBN 9783110263404
    Weitere Ausg.: ISBN 9783119166225
    Sprache: Englisch
    Schlagwort(e): Electronic books
    URL: Cover
    URL: Volltext  (URL des Erstveröffentlichers)
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Cover
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    UID:
    almahu_BV041105555
    Umfang: XI, 372 S. ; , 240 mm x 170 mm.
    ISBN: 3-11-026340-8 , 978-3-11-026340-4 , 978-3-11-916622-5
    Serie: De Gruyter Studies in Mathematics 49
    Anmerkung: Literaturverz. S. [335] - 360
    Weitere Ausg.: Erscheint auch als Online-Ausgabe ISBN 978-3-11-026401-2
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Schlagwort(e): Einbettung ; Diskreter metrischer Raum ; Banach-Raum
    Mehr zum Autor: Ostrovskii, Mikhail I.
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Online-Ressource
    Online-Ressource
    Berlin [u.a.] : De Gruyter
    UID:
    gbv_1656040530
    Umfang: Online-Ressource (XI, 372 S.)
    Ausgabe: Reproduktion 2013
    ISBN: 9783110264012
    Serie: De Gruyter Studies in Mathematics 49
    Inhalt: Biographical note: Mikhail I. Ostrovskii, St. John's University, Queens,USA.
    Inhalt: 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.
    Anmerkung: Description based upon print version of record , Preface; 1 Introduction: examples of metrics, embeddings, and applications; 1.1 Metric spaces: definitions and main examples; 1.2 Types of embeddings: isometric, bilipschitz, coarse, and uniform; 1.2.1 Isometric embeddings; 1.2.2 Bilipschitz embeddings; 1.2.3 Coarse and uniform embeddings; 1.3 Probability theory terminology and notation; 1.4 Applications to the sparsest cut problem; 1.5 Exercises; 1.6 Notes and remarks; 1.6.1 To Section 1.1; 1.6.2 To Section 1.2; 1.6.3 To Section 1.3; 1.6.4 To Section 1.4; 1.6.5 To exercises; 1.7 On applications in topology; 1.8 Hints to exercises , 2 Embeddability of locally finite metric spaces into Banach spaces is finitely determined. Related Banach space theory2.1 Introduction; 2.2 Banach space theory: ultrafilters, ultraproducts, finite representability; 2.2.1 Ultrafilters; 2.2.2 Ultraproducts; 2.2.3 Finite representability; 2.3 Proofs of the main results on relations between embeddability of a locally finite metric space and its finite subsets; 2.3.1 Proof in the bilipschitz case; 2.3.2 Proof in the coarse case; 2.3.3 Remarks on extensions of finite determination results , 2.4 Banach space theory: type and cotype of Banach spaces, Khinchin and Kahane inequalities2.4.1 Rademacher type and cotype; 2.4.2 Kahane-Khinchin inequality; 2.4.3 Characterization of spaces with trivial type or cotype; 2.5 Some corollaries of the theorems on finite determination of embeddability of locally finite metric spaces; 2.6 Exercises; 2.7 Notes and remarks; 2.8 Hints to exercises; 3 Constructions of embeddings; 3.1 Padded decompositions and their applications to constructions of embeddings; 3.2 Padded decompositions of minor-excluded graphs , 3.3 Padded decompositions in terms of ball growth3.4 Gluing single-scale embeddings; 3.5 Exercises; 3.6 Notes and remarks; 3.7 Hints to exercises; 4 Obstacles for embeddability: Poincaré inequalities; 4.1 Definition of Poincaré inequalities for metric spaces; 4.2 Poincaré inequalities for expanders; 4.3 Lp-distortion in terms of constants in Poincaré inequalities; 4.4 Euclidean distortion and positive semidefinite matrices; 4.5 Fourier analytic method of getting Poincaré inequalities; 4.6 Exercises; 4.7 Notes and remarks; 4.8 A bit of history of coarse embeddability; 4.9 Hints to exercises , 5 Families of expanders and of graphs with large girth5.1 Introduction; 5.2 Spectral characterization of expanders; 5.3 Kazhdan's property (T) and expanders; 5.4 Groups with property (T); 5.4.1 Finite generation of SLn(ℤ); 5.4.2 Finite quotients of SLn(ℤ); 5.4.3 Property (T) for groups SLn(ℤ); 5.4.4 Criterion for property (T); 5.5 Zigzag products; 5.6 Graphs with large girth: basic definitions; 5.7 Graph lift constructions and ℓ1-embeddable graphs with large girth; 5.8 Probabilistic proof of existence of expanders; 5.9 Size and diameter of graphs with large girth: basic facts , 5.10 Random constructions of graphs with large girth , Preface; 1 Introduction: examples of metrics, embeddings, and applications; 1.1 Metric spaces: definitions and main examples; 1.2 Types of embeddings: isometric, bilipschitz, coarse, and uniform; 1.2.1 Isometric embeddings; 1.2.2 Bilipschitz embeddings; 1.2.3 Coarse and uniform embeddings; 1.3 Probability theory terminology and notation; 1.4 Applications to the sparsest cut problem; 1.5 Exercises; 1.6 Notes and remarks; 1.6.1 To Section 1.1; 1.6.2 To Section 1.2; 1.6.3 To Section 1.3; 1.6.4 To Section 1.4; 1.6.5 To exercises; 1.7 On applications in topology; 1.8 Hints to exercises , 2 Embeddability of locally finite metric spaces into Banach spaces is finitely determined. Related Banach space theory2.1 Introduction; 2.2 Banach space theory: ultrafilters, ultraproducts, finite representability; 2.2.1 Ultrafilters; 2.2.2 Ultraproducts; 2.2.3 Finite representability; 2.3 Proofs of the main results on relations between embeddability of a locally finite metric space and its finite subsets; 2.3.1 Proof in the bilipschitz case; 2.3.2 Proof in the coarse case; 2.3.3 Remarks on extensions of finite determination results , 2.4 Banach space theory: type and cotype of Banach spaces, Khinchin and Kahane inequalities2.4.1 Rademacher type and cotype; 2.4.2 Kahane-Khinchin inequality; 2.4.3 Characterization of spaces with trivial type or cotype; 2.5 Some corollaries of the theorems on finite determination of embeddability of locally finite metric spaces; 2.6 Exercises; 2.7 Notes and remarks; 2.8 Hints to exercises; 3 Constructions of embeddings; 3.1 Padded decompositions and their applications to constructions of embeddings; 3.2 Padded decompositions of minor-excluded graphs , 3.3 Padded decompositions in terms of ball growth3.4 Gluing single-scale embeddings; 3.5 Exercises; 3.6 Notes and remarks; 3.7 Hints to exercises; 4 Obstacles for embeddability: Poincaré inequalities; 4.1 Definition of Poincaré inequalities for metric spaces; 4.2 Poincaré inequalities for expanders; 4.3 Lp-distortion in terms of constants in Poincaré inequalities; 4.4 Euclidean distortion and positive semidefinite matrices; 4.5 Fourier analytic method of getting Poincaré inequalities; 4.6 Exercises; 4.7 Notes and remarks; 4.8 A bit of history of coarse embeddability; 4.9 Hints to exercises , 5 Families of expanders and of graphs with large girth5.1 Introduction; 5.2 Spectral characterization of expanders; 5.3 Kazhdan's property (T) and expanders; 5.4 Groups with property (T); 5.4.1 Finite generation of SLn(ℤ); 5.4.2 Finite quotients of SLn(ℤ); 5.4.3 Property (T) for groups SLn(ℤ); 5.4.4 Criterion for property (T); 5.5 Zigzag products; 5.6 Graphs with large girth: basic definitions; 5.7 Graph lift constructions and ℓ1-embeddable graphs with large girth; 5.8 Probabilistic proof of existence of expanders; 5.9 Size and diameter of graphs with large girth: basic facts , 5.10 Random constructions of graphs with large girth , In English
    Weitere Ausg.: ISBN 9783110263404
    Weitere Ausg.: ISBN 9783110264012
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-3-11-026401-2
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe Ostrovskii, Mikhail I. Metric embeddings Berlin : de @Gruyter, 2013 ISBN 9783119166225
    Weitere Ausg.: ISBN 3110263408
    Weitere Ausg.: ISBN 9783110263404
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Schlagwort(e): Einbettung ; Diskreter metrischer Raum ; Banach-Raum ; Electronic books
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Cover
    Mehr zum Autor: Ostrovskii, Mikhail I.
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Buch
    Buch
    Berlin [u.a.] : Walter de Gruyter & Co.
    UID:
    kobvindex_ZLB15680010
    Umfang: XI, 372 Seiten
    ISBN: 978-3-11-026340-4 , 3-11-026340-8
    Serie: De Gruyter studies in mathematics 49
    Anmerkung: Literaturangaben
    Sprache: Englisch
    Mehr zum Autor: Ostrovskii, Mikhail I.
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 5
    Online-Ressource
    Online-Ressource
    Berlin :De Gruyter,
    UID:
    almahu_9948318001902882
    Umfang: 1 online resource (384 pages)
    ISBN: 9783110264012 (e-book)
    Serie: De Gruyter studies in mathematics
    Sprache: Englisch
    Schlagwort(e): Electronic books.
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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