An introduction to harmonic analysis on semisimple Lie groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1989
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 316 S. |
| ISBN: | 0521341566 |
Staff View
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| 100 | 1 | |a Varadarajan, V. S. |d 1937-2019 |e Verfasser |0 (DE-588)121025845 |4 aut | |
| 245 | 1 | 0 | |a An introduction to harmonic analysis on semisimple Lie groups |c V. S. Varadarajan |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1989 | |
| 300 | |a X, 316 S. | ||
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 16 | |
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| 650 | 7 | |a Représentations de groupes |2 ram | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Representations of Lie groups | |
| 650 | 4 | |a Semisimple Lie groups | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
1 Introduction t
1.1 Aim 1
1.2 Some definitions 1
1.3 Classical invariant theory 3
1.4 Quantum mechanics and unitary representations 4
1.5 Classical Fourier analysis, Plancherel and Poisson formulae 5
1.6 Fourier analysis on abelian groups 10
1.7 Harmonic analysis and arithmetic 13
Notes and comments 16
Problems 17
2 Compact groups: the work of Weyl 18
2.1 Characters. Orthogonality relations 18
2.2 The Peter Weyl theorem 19
2.3 Weyl s character formula for U(n) 23
2.4 Plancherel formula and orbital integrals for U{n) 32
2.5 Weyl s theory 35
2.6 The infinitesimal approach 41
2.7 Compact groups and complex groups. Unitarian trick 49
Notes and comments 53
Problems 53
3 Unitary representations of locally compact groups 55
3.1 Brief history 55
3.2 Haar measures on groups and homogeneous spaces 55
3.3 Induced representations 57
3.4 Semidirect products 63
3.5 Factor representations 64
4 Parabolic induction, principal series representations, and their characters 67
4.1 Early work 67
4.2 Parabolic subgroups and principal series for complex groups 68
4.3 Real groups: the Harish Chandra perspective 74
4.4 Character calculations 80
Notes and comments 99
Problems 99
5 Representations of the Lie algebra 100
5.1 Preliminaries on Lie algebras and enveloping algebras 100
5.2 Analytic vectors and the Harish Chandra density theorem 105
5.3 Representations of the Lie algebra. Finiteness and density theorems 111
5.4 Some consequences: finiteness of multiplicity, (g, K) modules, existence of
characters 118
5.5 Some explicit calculations 129
viii Contents
5.6 Remarks on proofs 140
Notes and comments 152
Problems 152
6 The Plancherel formula: character form 154
6.1 Plancherel formula for complex groups 154
6.2 Orbital integrals for G = SL(2, R) and g = sl(2, R) 167
6.3 Radial components of invariant differential operators on G and g and their
relation to orbital integrals 177
6.4 Behaviour of orbital integrals near singular points. The limit formulae 182
6.5 The discrete series. The modules Dm and their characters 187
6.6 The Plancherel formula for SU.2, R) 202
Problems 206
7 Invariant eigendistributions 208
7.1 Invariant eigendistributions and their behaviour on the regular set 208
7.2 Matching conditions 211
7.3 The Harish Chandra regularity theorem 215
Problems 220
8 Harmonic analysis of the Schwartz space 221
8.1 The point of view of differential equations and eigenfunction expansions.
Plancherel measure and its relation to eigenfunction asymptotics 221
8.2 Definition and the elementary theory of the Schwartz space 226
8.3 Asymptotic behaviour of matrix elements 233
8.4 The wave packet theorem 240
8.5 The Harish Chandra transform on the spaces ^mn 241
8.6 The relation /3(n) = 2n3n2 c*„(//)|2 and the determination of c*n 246
8.7 Exact wave packets. The Plancherel measure revisited 255
8.8 Tempered distributions. Temperedness of matrix elements, characters, and
conjugacy classes 260
8.9 Plancherel formula in Schwartz space 270
8.10 Completeness theorems 271
8.11 The Harish Chandra transform on 6(G) 272
8.12 Coda 282
Problems 290
Appendix 1 Functional analysis 291
A 1.1 Generalities 291
A 1.2 Spectral theory 291
A 1.3 Operators of Hilbert Schmidt and trace class 295
A 1.4 Distributions 296
A 1.5 Von Neumann algebras 299
Appendix 2 Topological groups 301
A2.1 Locally compact groups and Haar measure 301
Appendix 3 Lie groups and Lie algebras 302
A3.1 Basics 302
A3.2 Universal enveloping algebras 304
A3.3 Fundamental theorem of Lie 305
A3.4 Integration: distributions 306
A3.5 Semisimple Lie groups and Lie algebras 308
References 310
Subject index
|
| any_adam_object | 1 |
| author | Varadarajan, V. S. 1937-2019 |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| isbn | 0521341566 |
| language | English |
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| spelling | Varadarajan, V. S. 1937-2019 Verfasser (DE-588)121025845 aut An introduction to harmonic analysis on semisimple Lie groups V. S. Varadarajan 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1989 X, 316 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 16 Analyse harmonique Analyse harmonique ram Lie, Groupes de, semi-simples Représentations de groupes Représentations de groupes ram Harmonic analysis Representations of Lie groups Semisimple Lie groups Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Halbeinfache Lie-Gruppe (DE-588)4122188-6 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Cambridge studies in advanced mathematics 16 (DE-604)BV000003678 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002267623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Varadarajan, V. S. 1937-2019 An introduction to harmonic analysis on semisimple Lie groups Cambridge studies in advanced mathematics Analyse harmonique Analyse harmonique ram Lie, Groupes de, semi-simples Représentations de groupes Représentations de groupes ram Harmonic analysis Representations of Lie groups Semisimple Lie groups Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4122188-6 (DE-588)4023453-8 (DE-588)4035695-4 |
| title | An introduction to harmonic analysis on semisimple Lie groups |
| title_auth | An introduction to harmonic analysis on semisimple Lie groups |
| title_exact_search | An introduction to harmonic analysis on semisimple Lie groups |
| title_full | An introduction to harmonic analysis on semisimple Lie groups V. S. Varadarajan |
| title_fullStr | An introduction to harmonic analysis on semisimple Lie groups V. S. Varadarajan |
| title_full_unstemmed | An introduction to harmonic analysis on semisimple Lie groups V. S. Varadarajan |
| title_short | An introduction to harmonic analysis on semisimple Lie groups |
| title_sort | an introduction to harmonic analysis on semisimple lie groups |
| topic | Analyse harmonique Analyse harmonique ram Lie, Groupes de, semi-simples Représentations de groupes Représentations de groupes ram Harmonic analysis Representations of Lie groups Semisimple Lie groups Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Analyse harmonique Lie, Groupes de, semi-simples Représentations de groupes Harmonic analysis Representations of Lie groups Semisimple Lie groups Halbeinfache Lie-Gruppe Harmonische Analyse Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002267623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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