Holdings: Discrete groups, expanding graphs and invariant measures

Discrete groups, expanding graphs and invariant measures:

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Bibliographic Details
Main Authors:	Lubotzky, Alexander (Author), Rogawski, Jonathan D. (Author)
Format:	Book
Language:	English
Published:	Basel [u.a.] Birkhäuser 2010
Edition:	Reprint of the 1994 ed.
Series:	Modern Birkhäuser Classics
Subjects:	Invariantes Maß Expandierender Graph Lie-Gruppe
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XI, 192 S.
ISBN:	9783034603317 9783034603324

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MARC


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adam_text	IMAGE 1 TABLE OF CONTENTS 0 INTRODUCTION IX 1 EXPANDING GRAPHS 1.0 INTRODUCTION 1 1.1 EXPANDERS AND THEIR APPLICATIONS 1 1.2 EXISTENCE OF EXPANDERS 5 2 THE BANACH-RUZIEWICZ PROBLEM 2.0 INTRODUCTION 7 2.1 THE HAUSDORFF-BANACH-TARSKI PARADOX 7 2.2 INVARIANT MEASURES 13 2.3 NOTES 18 3 KAZHDAN PROPERTY (T) AND ITS APPLICATIONS 3.0 INTRODUCTION 19 3.1 KAZHDAN PROPERTY (T) FOR SEMI-SIMPLE GROUPS 19 3.2 LATTICES AND ARITHMETIC SUBGROUPS 27 3.3 EXPLICIT CONSTRUCTION OF EXPANDERS USING PROPERTY (T) 30 3.4 SOLUTION OF THE RUZIEWICZ PROBLEM FOR S N ,N 4 USING PROPERTY (T) 34 3.5 NOTES 39 4 THE LAPLACIAN AND ITS EIGENVALUES 4.0 INTRODUCTION 41 4.1 THE GEOMETRIC LAPLACIAN 41 4.2 THE COMBINATORIAL LAPLACIAN 44 4.3 EIGENVALUES, ISOPERIMETRIC INEQUALITIES AND REPRESENTATIONS . .. 49 4.4 SELBERG THEOREM AI ^ AND EXPANDERS 52 4.5 RANDOM WALK ON FC-REGULAR GRAPHS; RAMANUJAN GRAPHS 55 4.6 NOTES 59 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/996813802 DIGITALISIERT DURCH IMAGE 2 VI TABLE OF CONTENTS 5 THE REPRESENTATION THEORY OF PGL2 5.0 INTRODUCTION 61 5.1 REPRESENTATIONS AND SPHERICAL FUNCTIONS 62 5.2 IRREDUCIBLE REPRESENTATIONS OF PSL2(K) AND EIGENVALUES OF THE LAPLACIAN 65 5.3 THE TREE ASSOCIATED WITH PGL 2 {Q P ) 68 5.4 IRREDUCIBLE REPRESENTATIONS OF PGL2(QP) AND EIGENVALUES OF THE HECKE OPERATOR 70 5.5 SPECTRAL DECOMPOSITION OF T G 72 6 SPECTRAL DECOMPOSITION OF L 2 (G(Q) G(A)) 6.0 INTRODUCTION 77 6.1 DELIGNE S THEOREM; ADEIIC FORMULATION 77 6.2 QUATERNION ALGEBRAS AND GROUPS 79 6.3 THE STRONG APPROXIMATION THEOREM AND ITS APPLICATIONS 81 6.4 NOTES 83 7 BANACH-RUZIEWICZ PROBLEM FOR N = 2,3; RAMANUJAN GRAPHS 7.0 INTRODUCTION 85 7.1 THE SPECTRAL DECOMPOSITION OF G (Z[]) G (R) X G (Q P ) . . .. 86 7.2 THE BANACH-RUZIEWICZ PROBLEM FOR N = 2,3 86 7.3 RAMANUJAN GRAPHS AND THEIR EXTREMAL PROPERTIES 88 7.4 EXPLICIT CONSTRUCTIONS 94 7.5 NOTES 99 8 SOME MORE DISCRETE MATHEMATICS 8.0 INTRODUCTION 101 8.1 THE DIAMETER OF FINITE SIMPLE GROUPS 101 8.2 CHARACTERS AND EIGENVALUES OF FINITE GROUPS 106 8.3 SOME MORE RAMANUJAN GRAPHS (OF UNBOUNDED DEGREES) 112 8.4 RAMANUJAN DIAGRAMS 115 9 DISTRIBUTING POINTS ON THE SPHERE 9.0 INTRODUCTION 119 9.1 HECKE OPERATORS OF GROUP ACTION 119 9.2 DISTRIBUTING POINTS ON S 2 (AND S 3 ) 121 IMAGE 3 TABLE OF CONTENTS VII 10 OPEN PROBLEMS 10.1 EXPANDING GRAPHS 125 10.2 THE BANACH-RUZIEWICZ PROBLEM 125 10.3 KAZHDAN PROPERTY (T) AND ITS APPLICATIONS 126 10.4 THE LAPLACIAN AND ITS EIGENVALUES 128 10.5 THE REPRESENTATION THEORY OF PGL 2 129 10.6 SPECTRAL DECOMPOSITION OF L 2 (G(Q)/G(A)) 129 10.7 BANACH-RUZIEWITZ PROBLEM FOR N = 2,3; RAMANUJAN GRAPHS .. 130 10.8 SOME MORE DISCRETE MATHEMATICS 131 10.9 DISTRIBUTING POINTS ON THE SPHERE 133 APPENDIX: BY JONATHAN D. ROGOWSKI MODULAR FORMS, THE RAMANUJAN CONJECTURE AND THE JACQUET-LANGLANDS CORRESPONDENCE A.O PRELIMINARIES 136 A. 1 REPRESENTATION THEORY AND MODULAR FORMS 139 A.2 CLASSIFICATION OF IRREDUCIBLE REPRESENTATIONS 149 A.3 QUATERNION ALGEBRAS 159 A.4 THE SELBERG TRACE FORMULA 164 REFERENCES TO THE APPENDIX 175 REFERENCES 177 INDEX 193
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author	Lubotzky, Alexander Rogawski, Jonathan D.
author_facet	Lubotzky, Alexander Rogawski, Jonathan D.
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dewey-full	512.2
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	512 - Algebra
dewey-raw	512.2
dewey-search	512.2
dewey-sort	3512.2
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	Reprint of the 1994 ed.
format	Book
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indexdate	2024-07-09T23:21:27Z
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isbn	9783034603317 9783034603324
language	English
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physical	XI, 192 S.
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series2	Modern Birkhäuser Classics
spelling	Lubotzky, Alexander Verfasser aut Discrete groups, expanding graphs and invariant measures Alexander Lubotzky Reprint of the 1994 ed. Basel [u.a.] Birkhäuser 2010 XI, 192 S. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser Classics Invariantes Maß (DE-588)4352361-4 gnd rswk-swf Expandierender Graph (DE-588)4352360-2 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Expandierender Graph (DE-588)4352360-2 s Invariantes Maß (DE-588)4352361-4 s DE-604 Rogawski, Jonathan D. aut Modular forms, the Ramanujan conjecture and the Jacquet-Langlands correspondence V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018693010&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022448177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lubotzky, Alexander Rogawski, Jonathan D. Discrete groups, expanding graphs and invariant measures Invariantes Maß (DE-588)4352361-4 gnd Expandierender Graph (DE-588)4352360-2 gnd Lie-Gruppe (DE-588)4035695-4 gnd
subject_GND	(DE-588)4352361-4 (DE-588)4352360-2 (DE-588)4035695-4
title	Discrete groups, expanding graphs and invariant measures
title_alt	Modular forms, the Ramanujan conjecture and the Jacquet-Langlands correspondence
title_auth	Discrete groups, expanding graphs and invariant measures
title_exact_search	Discrete groups, expanding graphs and invariant measures
title_full	Discrete groups, expanding graphs and invariant measures Alexander Lubotzky
title_fullStr	Discrete groups, expanding graphs and invariant measures Alexander Lubotzky
title_full_unstemmed	Discrete groups, expanding graphs and invariant measures Alexander Lubotzky
title_short	Discrete groups, expanding graphs and invariant measures
title_sort	discrete groups expanding graphs and invariant measures
topic	Invariantes Maß (DE-588)4352361-4 gnd Expandierender Graph (DE-588)4352360-2 gnd Lie-Gruppe (DE-588)4035695-4 gnd
topic_facet	Invariantes Maß Expandierender Graph Lie-Gruppe
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018693010&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022448177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT lubotzkyalexander discretegroupsexpandinggraphsandinvariantmeasures AT rogawskijonathand discretegroupsexpandinggraphsandinvariantmeasures

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