Analysis on symmetric cones:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Clarendon Press
1994
|
| Series: | Oxford mathematical monographs
Oxford science publications |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006792441&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XII, 382 S. |
| ISBN: | 0198534779 |
Staff View
MARC
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| 245 | 1 | 0 | |a Analysis on symmetric cones |c Jacques Faraut and Adam Korányi |
| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press |c 1994 | |
| 300 | |a XII, 382 S. | ||
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 176f 2001 A 9867 |
|---|---|
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| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010374351 |
| _version_ | 1821931154302828544 |
| adam_text | CONTENTS
Chapter I Symmetric cones
1 Convex cones 1
2 Examples 7
3 The characteristic function of a cone 10
4 Symmetric cones as Riemannian symmetric spaces 15
Exercises 18
Notes 23
Chapter II Jordan algebras
1 Definitions and first properties 24
2 The minimal polynomial 27
3 The quadratic representation 32
4 Derivations and automorphisms 35
Exercises 38
Notes 41
Chapter III Symmetric cones and Euclidean Jordan algebras
1 Euclidean Jordan algebras 42
2 The cone of squares in a Euclidean Jordan algebra 46
3 The Jordan algebra associated with a symmetric cone 49
4 Simple Euclidean Jordan algebras 51
5 The group G and the invariant metric 55
Exercises 58
Notes 61
Chapter IV The Peirce decomposition in a Jordan algebra
1 The Peirce decomposition 62
2 Systems of idempotents 68
3 Boundary structure of a symmetric cone 72
4 Jordan algebra representations 74
Exercises 77
Notes 80
Chapter V Classification of Euclidean Jordan algebras
1 Hurwitz algebras 81
2 The algebras Herm(m, A) 86
3 The classification 92
Exercises 98
Notes 99
ix
x Contents
Chapter VI Polar decomposition and Gauss decomposition
1 Derivations and automorphisms revisited 100
2 Polar decomposition 102
3 Gauss decomposition 105
4 The Laplace Beltrami operator of a symmetric cone 115
Exercises 120
Notes 121
Chapter VII The gamma function of a symmetric cone
1 The gamma function 122
2 Riesz integrals 131
3 Positivity of the Riesz distributions 136
Exercises 141
Notes 142
Chapter VIII Complex Jordan algebras
1 Complexifications 144
2 The structure group of a semi simple Jordan algebra 146
3 Jordan canonical form 150
4 Formally real Jordan algebras 153
5 Existence of a Euclidean real form 154
Exercises 160
Notes 161
Chapter IX Tube domains over convex cones
1 Some definitions and basic facts 162
2 Reproducing kernel and Bergman kernel 164
3 The Bergman space of a tube domain 172
4 The Hardy space of a tube domain 178
5 Poisson kernel, Bergman Shilov boundary 181
Exercises 184
Notes 185
Chapter X Symmetric domains of tube type
1 The tube domain over a symmetric cone 187
2 The Cay ley transform 189
3 The group G(E) 193
4 The bounded domain D and its Shilov boundary 198
5 The automorphism groups G(Tq) and G(D) and their Lie algebras 204
Exercises 213
Notes 217
Contents xi
Chapter XI Conical and spherical polynomials
1 The Fischer inner product 220
2 Decomposition of the space of polynomials 223
3 Spherical polynomials 228
4 Norm computations 230
5 Expansion of some if invariant polynomials 234
Exercises 236
Notes 239
Chapter XII Taylor and Laurent series
1 Spherical Taylor series 240
2 Decomposition of the space I? (E) 245
3 Laurent series 249
Exercises 258
Notes 259
Chapter XIII Function spaces on symmetric domains of tube type
1 The spaces Hi 260
2 The Wallach set 264
3 Hardy spaces 269
4 Hua equations 276
Exercises 284
Notes 288
Chapter XIV Invariant differential operators and spherical functions
1 Invariant differential operators 290
2 The inner product in the spaces W^D) 298
3 Spherical functions 303
4 Spherical Fourier transform 307
5 The c function 311
Exercises 316
Notes 317
Chapter XV Special functions
1 Hypergeometric functions 318
2 Bessel functions 320
3 The Gauss hypergeometric functions 329
4 Hankel transform and Laguerre polynomials 341
Exercises 347
Notes 348
xii Contents
Chapter XVI Representations of Jordan algebras
and Euclidean Fourier analysis
1 Wishart distributions 349
2 Hankel transform 350
3 Generalized if Bessel functions 355
4 Zeta integrals 359
Exercises 362
Notes 363
Bibliography 364
Notation 378
Index 381
!
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| any_adam_object | 1 |
| author | Faraut, Jacques 1940- Korányi, Adam |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010220812 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:50:12Z |
| institution | BVB |
| isbn | 0198534779 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006792441 |
| oclc_num | 30593905 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-824 DE-384 DE-29T DE-19 DE-BY-UBM DE-20 DE-634 DE-11 |
| physical | XII, 382 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs Oxford science publications |
| spellingShingle | Faraut, Jacques 1940- Korányi, Adam Analysis on symmetric cones Kegels gtt Symmetrie gtt Álgebra larpcal Álgebras de jordan larpcal Cones (Operator theory) Harmonic analysis Jordan algebras Jordan-Algebra (DE-588)4162770-2 gnd Kegel (DE-588)4163534-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4162770-2 (DE-588)4163534-6 (DE-588)4023453-8 |
| title | Analysis on symmetric cones |
| title_auth | Analysis on symmetric cones |
| title_exact_search | Analysis on symmetric cones |
| title_full | Analysis on symmetric cones Jacques Faraut and Adam Korányi |
| title_fullStr | Analysis on symmetric cones Jacques Faraut and Adam Korányi |
| title_full_unstemmed | Analysis on symmetric cones Jacques Faraut and Adam Korányi |
| title_short | Analysis on symmetric cones |
| title_sort | analysis on symmetric cones |
| topic | Kegels gtt Symmetrie gtt Álgebra larpcal Álgebras de jordan larpcal Cones (Operator theory) Harmonic analysis Jordan algebras Jordan-Algebra (DE-588)4162770-2 gnd Kegel (DE-588)4163534-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Kegels Symmetrie Álgebra Álgebras de jordan Cones (Operator theory) Harmonic analysis Jordan algebras Jordan-Algebra Kegel Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006792441&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT farautjacques analysisonsymmetriccones AT koranyiadam analysisonsymmetriccones |
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| Call Number: |
0102 MAT 176f 2001 A 9867
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| Copy 1 | Available for loan On Shelf |