Causal symmetric spaces: geometry and harmonic analysis
During the last several years, a fairly complete structure theory of irreducible causal symmetric spaces has emerged. This book is the first to present this theory with exhaustive proofs. The final chapters provide an introduction to the applications of this topic to harmonic analysis
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
San Diego [u.a.]
Acad. Press
1997
|
| Schriftenreihe: | Perspectives in mathematics
18 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007417279&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | During the last several years, a fairly complete structure theory of irreducible causal symmetric spaces has emerged. This book is the first to present this theory with exhaustive proofs. The final chapters provide an introduction to the applications of this topic to harmonic analysis |
| Abstract: | This book introduces researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered "standard" by specialists have not been widely published. This book brings this information to students and researchers in geometry and analysis of causal symmetric spaces |
| Umfang: | XIV, 286 S. |
| ISBN: | 012525430X |
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| 520 | |a During the last several years, a fairly complete structure theory of irreducible causal symmetric spaces has emerged. This book is the first to present this theory with exhaustive proofs. The final chapters provide an introduction to the applications of this topic to harmonic analysis | ||
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Datensatz im Suchindex
| _version_ | 1824302207852347392 |
|---|---|
| adam_text |
CAUSAL SYMMETRIC SPACES GEOMETRY AND HARMONIC ANALYSIS JOACHIM HILGERT
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN GESTUR OLAFSSON
DEPARTMENT OF MATHEMATICS LOUISIANA STATE UNIVERSITY ACADEMIC PRESS SAN
DIEGO LONDON BOSTON NEW YORK SYDNEY TOKYO TORONTO CONTENTS PREFACE VIII
INTRODUCTION X 1 SYMMETRIC SPACES 1 1.1 BASIC STRUCTURE THEORY 1 1.2
DUAL SYMMETRIC SPACES 7 1.2.1 THE C-DUAL SPACE M C 7 1.2.2 THE
ASSOCIATED DUAL SPACE M" 9 1.2.3 THE RIEMANNIAN DUAL SPACE M R 9 1.3 THE
MODULE STRUCTURE OF T O (G/H) 12 1.4 A-SUBSPACES 22 1.5 THE HYPERBOLOIDS
24 2 CAUSAL ORIENTATIONS 29 2.1 CONVEX CONES AND THEIR AUTOMORPHISMS 29
2.2 CAUSAL ORIENTATIONS 39 2.3 SEMIGROUPS 43 2.4 THE ORDER
COMPACTIFICATION 45 2.5 EXAMPLES 50 2.5.1 THE GROUP CASE 50 2.5.2 THE
HYPERBOLOIDS 51 2.6 SYMMETRIC SPACES RELATED TO TUBE DOMAINS 52 2.6.1
BOUNDARY ORBITS 56 2.6.2 THE FUNCTIONS TF M 58 2.6.3 THE CAUSAL
COMPACTIFICATION OF M 63 2.6.4 SU(N,N) 65 2.6.5 SP(N,R) 68 VI CONTENTS 3
IRREDUCIBLE CAUSAL SYMMETRIC SPACES 71 3.1 EXISTENCE OF CAUSAL
STRUCTURES 71 3.2 THE CLASSIFICATION OF CAUSAL SYMMETRIC PAIRS 83 4
CLASSIFICATION OF INVARIANT CONES 91 4.1 SYMMETRIC SL(2, R) REDUCTION 91
4.2 THE MINIMAL AND MAXIMAL CONES 98 4.3 THE LINEAR CONVEXITY THEOREM
105 4.4 THE CLASSIFICATION 110 4.5 EXTENSION OF CONES 115 5 THE GEOMETRY
120 5.1 THE BOUNDED REALIZATION OF H/H D K 121 5.2 THE SEMIGROUP S(C)
126 5.3 THE CAUSAL INTERVALS 130 5.4 COMPRESSION SEMIGROUPS 132 5.5 THE
NONLINEAR CONVEXITY THEOREM 143 5.6 THE J3"-ORDER 152 5.7 THE AFFINE
CLOSURE OF B" 157 6 THE ORDER COMPACTIFICATION 172 6.1 CAUSAL GALOIS
CONNECTIONS 172 6.2 AN ALTERNATIVE REALIZATION OF M C /* 178 6.3 THE
STABILIZERS FOR M C F 180 6.4 THE ORBIT STRUCTURE OF M CPT 183 6.5 THE
SPACE SL(3,R)/SO(2,1) 190 7 HOLOMORPHIC REPRESENTATIONS 198 7.1
HOLOMORPHIC REPRESENTATIONS OF SEMIGROUPS 199 7.2 HIGHEST-WEIGHT MODULES
203 7.3 THE HOLOMORPHIC DISCRETE SERIES 209 7.4 CLASSICAL HARDY SPACES
214 7.5 HARDY SPACES 216 7.6 THE CAUCHY-SZEGO KERNEL 219 8 SPHERICAL
FUNCTIONS 222 8.1 THE CLASSICAL LAPLACE TRANSFORM 222 8.2 SPHERICAL
FUNCTIONS 224 8.3 THE ASYMPTOTICS 228 8.4 EXPANSION FORMULA 230 8.5 THE
SPHERICAL LAPLACE TRANSFORM 232 8.6 THE ABEL TRANSFORM 235 CONTENTS VII
8.7 RELATION TO REPRESENTATION THEORY 237 9 THE WIENER-HOPF ALGEBRA 239
A REDUCTIVE LIE GROUPS 246 A.I NOTATION 246 A.2 FINITE-DIMENSIONAL
REPRESENTATIONS 249 A.3 HERMITIAN GROUPS 252 B THE VIETORIS TOPOLOGY 257
NOTATION 262 BIBLIOGRAPHY 272 INDEX 284 |
| any_adam_object | 1 |
| author | Hilgert, Joachim Gestur Ólafsson 1952- |
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| callnumber-first | Q - Science |
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| classification_rvk | SK 340 SK 450 |
| ctrlnum | (OCoLC)35033580 (DE-599)BVBBV011073012 |
| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011073012 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-17T11:02:40Z |
| institution | BVB |
| isbn | 012525430X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007417279 |
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| physical | XIV, 286 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Acad. Press |
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| series | Perspectives in mathematics |
| series2 | Perspectives in mathematics |
| spelling | Hilgert, Joachim Verfasser aut Causal symmetric spaces geometry and harmonic analysis Joachim Hilgert ; Gestur Olafsson San Diego [u.a.] Acad. Press 1997 XIV, 286 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematics 18 This book introduces researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered "standard" by specialists have not been widely published. This book brings this information to students and researchers in geometry and analysis of causal symmetric spaces During the last several years, a fairly complete structure theory of irreducible causal symmetric spaces has emerged. This book is the first to present this theory with exhaustive proofs. The final chapters provide an introduction to the applications of this topic to harmonic analysis Analise harmonica larpcal Espaces symétriques ram Geometria diferencial larpcal Harmonic analysis Symmetric spaces Symmetrischer Raum (DE-588)4184206-6 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Symmetrischer Raum (DE-588)4184206-6 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Gestur Ólafsson 1952- Verfasser (DE-588)110569180 aut Perspectives in mathematics 18 (DE-604)BV000770492 18 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007417279&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hilgert, Joachim Gestur Ólafsson 1952- Causal symmetric spaces geometry and harmonic analysis Perspectives in mathematics Analise harmonica larpcal Espaces symétriques ram Geometria diferencial larpcal Harmonic analysis Symmetric spaces Symmetrischer Raum (DE-588)4184206-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4184206-6 (DE-588)4023453-8 |
| title | Causal symmetric spaces geometry and harmonic analysis |
| title_auth | Causal symmetric spaces geometry and harmonic analysis |
| title_exact_search | Causal symmetric spaces geometry and harmonic analysis |
| title_full | Causal symmetric spaces geometry and harmonic analysis Joachim Hilgert ; Gestur Olafsson |
| title_fullStr | Causal symmetric spaces geometry and harmonic analysis Joachim Hilgert ; Gestur Olafsson |
| title_full_unstemmed | Causal symmetric spaces geometry and harmonic analysis Joachim Hilgert ; Gestur Olafsson |
| title_short | Causal symmetric spaces |
| title_sort | causal symmetric spaces geometry and harmonic analysis |
| title_sub | geometry and harmonic analysis |
| topic | Analise harmonica larpcal Espaces symétriques ram Geometria diferencial larpcal Harmonic analysis Symmetric spaces Symmetrischer Raum (DE-588)4184206-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Analise harmonica Espaces symétriques Geometria diferencial Harmonic analysis Symmetric spaces Symmetrischer Raum Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007417279&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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