Discrete groups, expanding graphs and invariant measures:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2010
|
| Edition: | Reprint of the 1994 ed. |
| Series: | Progress in mathematics
125 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 192 S. |
| ISBN: | 9783034603317 9783034603324 |
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MARC
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| 100 | 1 | |a Lubotzky, Alexander |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Discrete groups, expanding graphs and invariant measures |c Alexander Lubotzky |
| 250 | |a Reprint of the 1994 ed. | ||
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2010 | |
| 300 | |a XI, 192 S. | ||
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| 700 | 1 | 2 | |a Rogawski, Jonathan D. |4 aut |t Modular forms, the Ramanujan conjecture and the Jacquet-Langlands correspondence |
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Record in the Search Index
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|---|---|
| adam_text | 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 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. 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
|
| any_adam_object | 1 |
| author | Lubotzky, Alexander Rogawski, Jonathan D. |
| author_facet | Lubotzky, Alexander Rogawski, Jonathan D. |
| author_role | aut aut |
| author_sort | Lubotzky, Alexander |
| author_variant | a l al j d r jd jdr |
| building | Verbundindex |
| bvnumber | BV035834550 |
| classification_rvk | SK 340 |
| classification_tum | MAT 103f |
| ctrlnum | (OCoLC)634995156 (DE-599)BVBBV035834550 |
| 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 | 2024-07-09T22:05:43Z |
| institution | BVB |
| isbn | 9783034603317 9783034603324 |
| language | English |
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| physical | XI, 192 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| 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 Progress in mathematics 125 Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Invariantes Maß (DE-588)4352361-4 gnd rswk-swf Expandierender Graph (DE-588)4352360-2 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 Progress in mathematics 125 (DE-604)BV000004120 125 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018693010&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 Progress in mathematics Lie-Gruppe (DE-588)4035695-4 gnd Invariantes Maß (DE-588)4352361-4 gnd Expandierender Graph (DE-588)4352360-2 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4352361-4 (DE-588)4352360-2 |
| 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 | Lie-Gruppe (DE-588)4035695-4 gnd Invariantes Maß (DE-588)4352361-4 gnd Expandierender Graph (DE-588)4352360-2 gnd |
| topic_facet | Lie-Gruppe Invariantes Maß Expandierender Graph |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018693010&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT lubotzkyalexander discretegroupsexpandinggraphsandinvariantmeasures AT rogawskijonathand discretegroupsexpandinggraphsandinvariantmeasures |