The ergodic theory of lattice subgroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, N.J.
Princeton Univ. Press
2010
|
| Series: | Annals of mathematics studies
172 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 120 S. |
| ISBN: | 9780691141848 9780691141855 |
Staff View
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| 100 | 1 | |a Gorodnik, Alexander |d 1975- |e Verfasser |0 (DE-588)13939463X |4 aut | |
| 245 | 1 | 0 | |a The ergodic theory of lattice subgroups |c Alexander Gorodnik and Amos Nevo |
| 264 | 1 | |a Princeton, N.J. |b Princeton Univ. Press |c 2010 | |
| 300 | |a XIII, 120 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Annals of mathematics studies |v 172 | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Dynamics | |
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Record in the Search Index
| _version_ | 1804140680547663872 |
|---|---|
| adam_text | Titel: The ergodic theory of lattice subgroups
Autor: Gorodnik, Alexander
Jahr: 2010
Contents
Preface v¡¡
0.1 Main objectives vii
0.2 Ergodic theory and amenable groups viii
0.3 Ergodic theory and nonamenable groups X
Chapter 1. Main results: Semisimple Lie groups case 1
1.1 Admissible sets 1
1.2 Ergodic theorems on semisimple Lie groups 2
1.3 The lattice point-counting problem in admissible domains 4
1.4 Ergodic theorems for lattice subgroups 6
1.5 Scope of the method 8
Chapter 2. Examples and applications 11
2.1 Hyperbolic lattice points problem , 11
2.2 Counting integral unimodular matrices 12
2.3 Integral equivalence of general forms 13
2.4 Lattice points in 5-algebraic groups 15
2.5 Examples of ergodic theorems for lattice actions 16
Chapter 3. Definitions, preliminaries, and basic tools 19
3.1 Maximal and exponential-maximal inequalities 19
3.2 5-algebraic groups and upper local dimension 21
3.3 Admissible and coarsely admissible sets 21
3.4 Absolute continuity and examples of admissible averages 23
3.5 Balanced and well-balanced families on product groups 26
3.6 Roughly radial and quasi-uniform sets 27
3.7 Spectral gap and strong spectral gap 29
3.8 Finite-dimensional subrepresentations 30
Chapter 4. Main results and an overview of the proofs 33
4.1 Statement of ergodic theorems for 5-algebraic groups 33
4.2 Ergodic theorems in the absence of a spectral gap: overview 35
4.3 Ergodic theorems in the presence of a spectral gap: overview 38
4.4 Statement of ergodic theorems for lattice subgroups 40
4.5 Ergodic theorems for lattice subgroups: overview 42
4.6 Volume regularity and volume asymptotics: overview 44
V¡ CONTENTS
Chapter 5. Proof of ergodic theorems for S-algebraic groups 47
5.1 Iwasawa groups and spectral estimates 47
5.2 Ergodic theorems in the presence of a spectral gap 50
5.3 Ergodic theorems in the absence of a spectral gap, I 56
5.4 Ergodic theorems in the absence of a spectral gap, II 57
5.5 Ergodic theorems in the absence of a spectral gap, III 60
5.6 The invariance principle and stability of admissible averages 67
Chapter 6. Proof of ergodic theorems for lattice subgroups 71
6.1 Induced action 71
6.2 Reduction theorems 74
6.3 Strong maximal inequality 75
6.4 Mean ergodic theorem 78
6.5 Pointwise ergodic theorem 83
6.6 Exponential mean ergodic theorem 84
6.7 Exponential strong maximal inequality 87
6.8 Completion of the proofs 90
6.9 Equidistribution in isometric actions 91
Chapter 7. Volume estimates and volume regularity 93
7.1 Admissibility of standard averages 93
7.2 Convolution arguments 98
7.3 Admissible, well-balanced, and boundary-regular families 101
7.4 Admissible sets on principal homogeneous spaces 105
7.5 Tauberian arguments and Holder continuity 107
Chapter 8. Comments and complements 113
8.1 Lattice point-counting with explicit error term 113
8.2 Exponentially fast convergence versus equidistribution 115
83 Remark about balanced sets 116
Bibliography il7
Index 121
|
| any_adam_object | 1 |
| author | Gorodnik, Alexander 1975- |
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| id | DE-604.BV035758318 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:50Z |
| institution | BVB |
| isbn | 9780691141848 9780691141855 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018618240 |
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| physical | XIII, 120 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Gorodnik, Alexander 1975- Verfasser (DE-588)13939463X aut The ergodic theory of lattice subgroups Alexander Gorodnik and Amos Nevo Princeton, N.J. Princeton Univ. Press 2010 XIII, 120 S. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 172 Includes bibliographical references and index Ergodic theory Lie groups Lattice theory Harmonic analysis Dynamics Nevo, Amos 1966- Sonstige (DE-588)139394656 oth Annals of mathematics studies 172 (DE-604)BV000000991 172 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018618240&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gorodnik, Alexander 1975- The ergodic theory of lattice subgroups Annals of mathematics studies Ergodic theory Lie groups Lattice theory Harmonic analysis Dynamics |
| title | The ergodic theory of lattice subgroups |
| title_auth | The ergodic theory of lattice subgroups |
| title_exact_search | The ergodic theory of lattice subgroups |
| title_full | The ergodic theory of lattice subgroups Alexander Gorodnik and Amos Nevo |
| title_fullStr | The ergodic theory of lattice subgroups Alexander Gorodnik and Amos Nevo |
| title_full_unstemmed | The ergodic theory of lattice subgroups Alexander Gorodnik and Amos Nevo |
| title_short | The ergodic theory of lattice subgroups |
| title_sort | the ergodic theory of lattice subgroups |
| topic | Ergodic theory Lie groups Lattice theory Harmonic analysis Dynamics |
| topic_facet | Ergodic theory Lie groups Lattice theory Harmonic analysis Dynamics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018618240&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT gorodnikalexander theergodictheoryoflatticesubgroups AT nevoamos theergodictheoryoflatticesubgroups |