Classical harmonic analysis and locally compact groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Clarendon Press
2000
|
| Edition: | 2. ed. |
| Series: | London Mathematical Society: [London Mathematical Society monographs / New series]
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 327 S. |
| ISBN: | 9780198511892 0198511892 |
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MARC
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| 100 | 1 | |a Reiter, Hans |d 1921-1992 |e Verfasser |0 (DE-588)1029676399 |4 aut | |
| 245 | 1 | 0 | |a Classical harmonic analysis and locally compact groups |c Hans Reiter ; Jan D. Stegeman |
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| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press |c 2000 | |
| 300 | |a XIII, 327 S. | ||
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Record in the Search Index
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| adam_text | Contents
Reader s guide xi
1 Classical harmonic analysis and Wiener s theorem 1
1.1 The algebra L (Kv); Fourier transforms 1
1.2 Functions in LX(W) 7
1.3 The Wiener Levy theorem 10
1.4 Wiener s theorem 12
1.5 SomesubalgebrasofL PD 16
1.6 The algebras L^(RV); Beurling algebras 18
2 Function algebras and the generalization of Wiener s theorem 25
2.1 Function algebras 25
2.2 Topological function algebras and Wiener s theorem 28
2.3 Examples of topological function algebras 31
2.4 The generalization of Wiener s theorem 35
2.5 Ditkin sets for function algebras 40
2.6 Ideals in function algebras; examples 44
2.7 Sets of spectral synthesis; examples, counter examples 49
3 Locally compact groups and the Haar measure 56
3.1 Locally compact groups 56
3.2 Integration on locally compact spaces 61
3.3 The Haar measure 82
3.4 L spaces on groups 97
3.5 The algebra O{G) 104
3.6 The space L°°(G) 113
3.7 Beurling algebras 119
4 Locally compact abelian groups and the foundations of harmonic
analysis 128
4.1 Locally compact abelian groups 128
4.2 Duality theory and structure theory 132
4.3 Some examples 138
4.4 The foundations of harmonic analysis 143
4.5 The principle of relativization 150
x Contents
5 Functions on locally compact abelian groups 152
5.1 The functions a and t 152
5.2 Lemmas on functions in Ll(G) 155
5.3 Lemmas on functions in Ll(G) (continued) 159
5.4 Some properties of L (G) and Tx (G) 160
5.5 Poisson s formula 164
6 Wiener s theorem and locally compact abelian groups 169
6.1 Wiener s theorem for groups 169
6.2 Segal algebras, the abelian case 173
6.3 Beurling algebras 184
7 The spectrum and its applications 194
7.1 Definition and properties of the spectrum 194
7.2 Relativization and the spectrum 200
7.3 Sets of spectral synthesis for Beurling algebras 203
7.4 Ditkin sets on groups 212
8 Functions on general locally compact groups 221
8.1 Quasi invariant measures on quotient spaces 221
8.2 The space L (G/H) 230
8.3 The property Pp 234
8.4 The invariant convex hull of a function in L (G) 242
8.5 The property (M) 247
8.6 The equivalence of the properties (M) and Pi 251
8.7 The structure of groups with the property Pi 256
A Additional material 262
A.I Domar s theorem 262
A.2 Malliavin s theorem 267
A.3 More on Segal algebras 272
A.4 The difference spectrum 282
B Notes and additional references 293
References 302
Summary of notations 316
Subject index 321
|
| any_adam_object | 1 |
| author | Reiter, Hans 1921-1992 Stegeman, Jan Derk 1936- |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013484762 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:40Z |
| institution | BVB |
| isbn | 9780198511892 0198511892 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009203959 |
| oclc_num | 44018888 |
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| physical | XIII, 327 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | London Mathematical Society: [London Mathematical Society monographs / New series] |
| spelling | Reiter, Hans 1921-1992 Verfasser (DE-588)1029676399 aut Classical harmonic analysis and locally compact groups Hans Reiter ; Jan D. Stegeman 2. ed. Oxford [u.a.] Clarendon Press 2000 XIII, 327 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: [London Mathematical Society monographs / New series] 22 Harmonic analysis Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Topologische Gruppe (DE-588)4135793-0 s Lokal kompakte Gruppe (DE-588)4168094-7 s Stegeman, Jan Derk 1936- Verfasser (DE-588)1029702918 aut New series] London Mathematical Society: [London Mathematical Society monographs 22 (DE-604)BV045355493 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203959&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reiter, Hans 1921-1992 Stegeman, Jan Derk 1936- Classical harmonic analysis and locally compact groups Harmonic analysis Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4168094-7 (DE-588)4023453-8 (DE-588)4135793-0 |
| title | Classical harmonic analysis and locally compact groups |
| title_auth | Classical harmonic analysis and locally compact groups |
| title_exact_search | Classical harmonic analysis and locally compact groups |
| title_full | Classical harmonic analysis and locally compact groups Hans Reiter ; Jan D. Stegeman |
| title_fullStr | Classical harmonic analysis and locally compact groups Hans Reiter ; Jan D. Stegeman |
| title_full_unstemmed | Classical harmonic analysis and locally compact groups Hans Reiter ; Jan D. Stegeman |
| title_short | Classical harmonic analysis and locally compact groups |
| title_sort | classical harmonic analysis and locally compact groups |
| topic | Harmonic analysis Locally compact groups Lokal kompakte Gruppe (DE-588)4168094-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Harmonic analysis Locally compact groups Lokal kompakte Gruppe Harmonische Analyse Topologische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009203959&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
| work_keys_str_mv | AT reiterhans classicalharmonicanalysisandlocallycompactgroups AT stegemanjanderk classicalharmonicanalysisandlocallycompactgroups |