Introduction to harmonic analysis and generalized Gelfand pairs:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2009
|
| Schriftenreihe: | De Gruyter Studies in Mathematics
36 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3360096&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018677589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | IX, 223 S. Ill. |
| ISBN: | 9783110220193 |
Internformat
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| 245 | 1 | 0 | |a Introduction to harmonic analysis and generalized Gelfand pairs |c Gerrit van Dijk |
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| 650 | 4 | |a Harmonic analysis | |
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Datensatz im Suchindex
| _version_ | 1819356527619735552 |
|---|---|
| adam_text | 45 CONTENTS PREFACE V 1 FOURIER SERIES 1 1.1 DEFINITION AND ELEMENTARY
PROPERTIES 1 1.2 CONVERGENCE 2 1.3 UNIFORM CONVERGENCE 3 1.4 SOME FACTS
ABOUT CONVERGENCE OF FOURIER SERIES 5 1.5 PARSEVAL S THEOREM 5 1.6
GENERALIZATION 6 2 FOURIER INTEGRALS 7 2.1 THE CONVOLUTION PRODUCT 7 2.2
ELEMENTARY PROPERTIES OF THE FOURIER INTEGRAL 8 2.3 THE INVERSION
THEOREM 9 2.4 PLANCHEREL S THEOREM 12 2.5 THE POISSON SUMMATION FORMULA
13 2.6 THE RIEMANN-STIELTJES INTEGRAL AND FUNCTIONS OF BOUNDED VARIATION
13 2.7 BOCHNER S THEOREM 19 2.8 EXTENSION TO W 24 3 LOCALLY COMPACT
GROUPS 25 3.1 GROUPS 25 3.2 TOPOLOGICAL SPACES 25 3.3 TOPOLOGICAL GROUPS
27 3.4 QUOTIENT SPACES AND QUOTIENT GROUPS 29 3.5 SOME USEFUL FACTS 30
3.6 FUNCTIONS ON LOCALLY COMPACT GROUPS 31 4 HAAR MEASURES 32 4.1
MEASURES 32 4.2 INVARIANT MEASURES 34 4.3 WEIL S FORMULA 39 4.4 HAAR
MEASURES FOR SPECIFIC GROUPS 41 4.5 QUASI-INVARIANT MEASURES ON QUOTIENT
SPACES 41 4.6 THE CONVOLUTION PRODUCT ON G. PROPERTIES OF L L (G)
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/997086378 DIGITALISIERT
DURCH VIII CONTENTS 5 HARMONIC ANALYSIS ON LOCALLY COMPACT ABELIAN
GROUPS 49 5.1 POSITIVE-DEFINITE FUNCTIONS AND UNITARY REPRESENTATIONS 49
5.2 SOME FUNCTIONAL ANALYSIS 55 5.3 ELEMENTARY POSITIVE-DEFINITE
FUNCTIONS 60 5.4 FOURIER TRANSFORM, RIEMANN-LEBESGUE LEMMA AND BOCHNER S
THE- OREM 62 5.5 THE INVERSION THEOREM 66 5.6 PLANCHEREL S THEOREM 69
5.7 PONTRYAGIN S DUALITY THEOREM 70 5.8 SUBGROUPS AND QUOTIENT GROUPS 73
5.9 COMPACT AND DISCRETE ABELIAN GROUPS 74 6 CLASSICAL THEORY OF GELFAND
PAIRS 75 6. 1 GELFAND PAIRS AND SPHERICAL FUNCTIONS 75 6.2
POSITIVE-DEFINITE SPHERICAL FUNCTIONS AND UNITARY REPRESENTATIONS . . 79
6.3 REPRESENTATIONS OF CLASS ONE 82 6.4 HARMONIC ANALYSIS ON GELFAND
PAIRS 83 6.5 COMPACT GELFAND PAIRS 86 7 EXAMPLES OF GELFAND PAIRS 89 7.1
EUCLIDEAN MOTION GROUPS 89 7.2 THE SPHERE 95 7.3 SPHERICAL HARMONICS 96
7.4 SPHERICAL FUNCTIONS ON SPHERES 105 7.5 REAL HYPERBOLIC SPACES 106 8
THEORY OF GENERALIZED GELFAND PAIRS 131 8.1 C VECTORS OF A
REPRESENTATION 131 8.2 INVARIANT HUBERT SUBSPACES 135 8.3 GENERALIZED
GELFAND PAIRS 141 8.4 INVARIANT HUBERT SUBSPACES OF L 2 (G/H) 145 9
EXAMPLES OF GENERALIZED GELFAND PAIRS 15 CONTENTS IX * THE AVERAGING
MAPPING ON THE SPACE X 210 B.I SPECIAL CASE OF A THEOREM OF
HARISH-CHANDRA 210 B.2 ANALOG OF METHEE S RESULTS 210 B.3 TENGSTRAND S
RESULTS FOR X 212 B.4 SOLUTIONS IN * * OF A SINGULAR SECOND ORDER
DIFFERENTIAL EQUATION . . 213 BIBLIOGRAPHY 217 INDEX 221
|
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV035818799 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:00:54Z |
| institution | BVB |
| isbn | 9783110220193 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018677589 |
| oclc_num | 456186278 |
| open_access_boolean | |
| owner | DE-824 DE-20 DE-634 DE-11 |
| owner_facet | DE-824 DE-20 DE-634 DE-11 |
| physical | IX, 223 S. Ill. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spellingShingle | Dijk, Gerrit van 1939- Introduction to harmonic analysis and generalized Gelfand pairs De Gruyter Studies in Mathematics Commutatieve algebra's gtt Convolutie gtt Fourier-integralen gtt Fourier-reeksen gtt Harmonische analyse gtt Topologische groepen gtt Fourier analysis Harmonic analysis Abstrakte harmonische Analysis (DE-588)4821471-1 gnd |
| subject_GND | (DE-588)4821471-1 |
| title | Introduction to harmonic analysis and generalized Gelfand pairs |
| title_auth | Introduction to harmonic analysis and generalized Gelfand pairs |
| title_exact_search | Introduction to harmonic analysis and generalized Gelfand pairs |
| title_full | Introduction to harmonic analysis and generalized Gelfand pairs Gerrit van Dijk |
| title_fullStr | Introduction to harmonic analysis and generalized Gelfand pairs Gerrit van Dijk |
| title_full_unstemmed | Introduction to harmonic analysis and generalized Gelfand pairs Gerrit van Dijk |
| title_short | Introduction to harmonic analysis and generalized Gelfand pairs |
| title_sort | introduction to harmonic analysis and generalized gelfand pairs |
| topic | Commutatieve algebra's gtt Convolutie gtt Fourier-integralen gtt Fourier-reeksen gtt Harmonische analyse gtt Topologische groepen gtt Fourier analysis Harmonic analysis Abstrakte harmonische Analysis (DE-588)4821471-1 gnd |
| topic_facet | Commutatieve algebra's Convolutie Fourier-integralen Fourier-reeksen Harmonische analyse Topologische groepen Fourier analysis Harmonic analysis Abstrakte harmonische Analysis |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3360096&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018677589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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