Analysis and geometry on groups:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2003
|
| Ausgabe: | transferred to digital print. |
| Schriftenreihe: | Cambridge tracts in mathematics
100 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017050948&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 148 - 155 |
| Umfang: | XII, 155 S. |
| ISBN: | 0521353823 9780521353823 |
Internformat
MARC
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| 245 | 1 | 0 | |a Analysis and geometry on groups |c N. Th. Varopoulos ; L. Saloff-Coste ; T. Coulhon |
| 250 | |a transferred to digital print. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XII, 155 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 100 | |
| 500 | |a Literaturverz. S. 148 - 155 | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017050948 | |
Datensatz im Suchindex
| _version_ | 1819275306940235776 |
|---|---|
| adam_text | CONTENTS
Preface
vii
Foreword
ix
I Introduction
1
1
Sobolev inequalities in Rn
1
2
Sobolev inequalities and the heat equation on Lie groups
3
3
Harnack s principle
5
4
A guide to this book
6
II Dimensional inequalities for semigroups of
operators on the IP spaces
8
1
Introduction, notation
8
2
Hardy-Littlewood-Sobolev theory
9
3
Converses to the Hardy-Littlewood-Sobolev theory
12
4
Localizations
17
5
Symmetric submarkovian semigroups
20
References and Comments
25
III Systems of vector fields satisfying
Hörmander s
condition
26
1 Hörmander s
condition and hypoellipticity
26
Uniformity matters
27
2
Harnack inequalities
28
Uniformity matters
32
3
The exponential map
34
4
Carnot-Carathéodory
distances
39
References and Comments
41
IV The heat kernel on
nilpotent
Lie groups
42
1
Some remarkable properties of
nilpotent
Lie groups
42
2
Examples
43
3
Harnack inequalities for
nilpotent
Lie groups
45
4
Estimates of the heat kernel
48
5
Estimates of the volume
50
β
Sobolev s theorem
55
7
Sobolev inequalities
56
References and Comments
61
V Local theory for sums of squares of vector fields
63
1
Estimates of the volume
63
2
Proof of the Key Lemma
65
3
Local scaling of the Harnack inequality
67
VI
4
The case of unimodulax Lie groups
69
5
The general case TO
References and Comments
72
VI Convolution powers on finitely generated groups
74
1
Introduction
74
2
Distance and volume growth function on a group
75
3
The main results for superpolynomial groups
77
4
Comparison of Dirichlet forms and finite variance
81
5 Nilpotent
finitely generated groups
84
6
Kesten s conjecture
85
References and Comments
86
VII
Convolution powers on unimodular
compactly generated groups
88
1
Main results
88
2
Dimension theory for symmetric submarkovian operators
89
3
Comparison of Dirichlet forms
94
4
Volume growth and polynomial decay of convolution powers
99
5
The case of superpolynomial growth
103
References and Comments
105
VIII
The heat kernel on unimodular Lie groups
106
1
Preliminaries
106
2
Polynomial growth Lie groups
107
3
Harnack inequalities for polynomial growth groups
114
4
Exponential growth Lie groups
119
References and Comments
122
IX Sobolev inequalities on non-imimodular Lie groups
123
1
Local theory
123
2
An inequality of Hardy and some consequences
128
3
A Sobolev inequality again
132
References and Comments
137
X Geometric applications
138
1
Geometry of Lie groups and quasiregular maps
138
2
Picard
theorems on Lie groups
139
3
Brownian motion on covering manifolds and
random walks on groups
141
4
Dimension at infinity of a covering manifold
143
5
Quasiregular maps and compact manifolds
146
References and Comments
147
Bibliography
148
Index
156
|
| any_adam_object | 1 |
| author | Varopoulos, N. Th. 1940- Saloff-Coste, Laurent 1958- Coulhon, Thierry 1958- |
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| callnumber-raw | QA387 |
| callnumber-search | QA387 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| classification_tum | MAT 200f |
| ctrlnum | (OCoLC)249395373 (DE-599)BVBBV035245218 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | transferred to digital print. |
| format | Book |
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| id | DE-604.BV035245218 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:26:45Z |
| institution | BVB |
| isbn | 0521353823 9780521353823 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017050948 |
| oclc_num | 249395373 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XII, 155 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spellingShingle | Varopoulos, N. Th. 1940- Saloff-Coste, Laurent 1958- Coulhon, Thierry 1958- Analysis and geometry on groups Cambridge tracts in mathematics Lie-Gruppe - Markov-Kette Lie-Gruppe (DE-588)4035695-4 gnd Analysis (DE-588)4001865-9 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4001865-9 (DE-588)4020236-7 |
| title | Analysis and geometry on groups |
| title_auth | Analysis and geometry on groups |
| title_exact_search | Analysis and geometry on groups |
| title_full | Analysis and geometry on groups N. Th. Varopoulos ; L. Saloff-Coste ; T. Coulhon |
| title_fullStr | Analysis and geometry on groups N. Th. Varopoulos ; L. Saloff-Coste ; T. Coulhon |
| title_full_unstemmed | Analysis and geometry on groups N. Th. Varopoulos ; L. Saloff-Coste ; T. Coulhon |
| title_short | Analysis and geometry on groups |
| title_sort | analysis and geometry on groups |
| topic | Lie-Gruppe - Markov-Kette Lie-Gruppe (DE-588)4035695-4 gnd Analysis (DE-588)4001865-9 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Lie-Gruppe - Markov-Kette Lie-Gruppe Analysis Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017050948&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT varopoulosnth analysisandgeometryongroups AT saloffcostelaurent analysisandgeometryongroups AT coulhonthierry analysisandgeometryongroups |