A course in abstract harmonic analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1995
|
| Schriftenreihe: | Studies in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 276 S. |
| ISBN: | 0849384907 |
Internformat
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| 100 | 1 | |a Folland, Gerald B. |d 1947- |e Verfasser |0 (DE-588)137062486 |4 aut | |
| 245 | 1 | 0 | |a A course in abstract harmonic analysis |c Gerald B. Folland |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 1995 | |
| 300 | |a VIII, 276 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Studies in advanced mathematics | |
| 650 | 4 | |a Analyse harmonique | |
| 650 | 7 | |a Analyse harmonique |2 ram | |
| 650 | 7 | |a Harmonische analyse |2 gtt | |
| 650 | 4 | |a Harmonic analysis | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
v
1
Banach
Algebras and Spectral Theory
1
1.1
Banach Algebras: Basic Concepts
.............. 1
1.2
Gelfand Theory
........................ 5
1.3
Nonunital Banach Algebras
................. 12
1.4
The Spectral Theorem
.................... 1*6
1.5
Spectral Theory of »-Representations
............ 26
1.6
Notes and References
..................... 28
2
Locally Compact Groups
31
2.1
Topological Groups
...................... 31
2.2 Haar
Measure
......................... 36
2.3
Interlude: Some Technicalities
...........-*..... 43
2.4
The Modular Function
.................... 46
2.5
Convolutions
......................... 49
2.6
Homogeneous Spaces
..................... 54
2.7
Notes and References
..................... 64
3
Basic Representation Theory
67
3.1
Unitary Representations
................... 67
3.2
Representations of a group and its group algebra
..... 73
3.3
Functions of Positive Type
.................. 76
3.4
Notes and References
..................... 86
4
Analysis on Locally Compact Abelian Groups
87
4.1
The Dual Group
.......................87
4.2
The Fourier Transform
....................93
4.3
The Pontrjagin Duality Theorem
..............100
4.4
Representations of Locally Compact Abelian Groups
. . . 105
4.5
Closed Ideals in I}{G)
....................107
4.6
Spectral Synthesis
......................116
4.7
The Bohr Compactification
.................119
4.8
Notes and References
.....................121
in
iv
A Course in Abstract Harmonic Analysis
5
Analysis on Compact Groups
125
5.1
Representations of Compact Groups
............125
5.2
The Peter-Weyl Theorem
..................128
5.3
Fourier Analysis on Compact Groups
............133
5.4
Examples
...........................139
5.5
Notes and References
.....................147
6
Induced Representations
151
6.1
The Inducing Construction
.................152
6.2
The Frobenius Reciprocity Theorem
............160
6.3
Pseudomeasures and Induction in Stages
..........162
6.4
Systems of Imprimitivity
...................167
6.5
The Imprimitivity Theorem
.................174
6.6
Introduction to the Mackey Machine
............182
6.7
Examples
...........................188
6.8
Notes and References
.....................197
7
Further Topics in Representation Theory
201
7.1
The Group C* Algebra
....................201
7.2
The Structure of the Dual Space
..............204
7.3
Tensor Products
.......................210
7.4
Direct Integral Decompositions
...............219
7.5
The Plancherel Theorem
...................232
7.6
Examples
...........................239
Appendices
253
1
A Hilbert Space Miscellany
.................253
2
Trace-Class and Hilbert-Schmidt Operators
........256
3
Vector-Valued Integrals
...................259
Bibliography
263
Index
271
List of Figures
7.1
The dual space of Hn
.....................240
7.2
The dual space of the ax + b group
.............242
7.3
The dual space of SL(2,H)
..................247
|
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:01:29Z |
| institution | BVB |
| isbn | 0849384907 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007321292 |
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| physical | VIII, 276 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | CRC Press |
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| series2 | Studies in advanced mathematics |
| spelling | Folland, Gerald B. 1947- Verfasser (DE-588)137062486 aut A course in abstract harmonic analysis Gerald B. Folland Boca Raton [u.a.] CRC Press 1995 VIII, 276 S. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics Analyse harmonique Analyse harmonique ram Harmonische analyse gtt Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007321292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Folland, Gerald B. 1947- A course in abstract harmonic analysis Analyse harmonique Analyse harmonique ram Harmonische analyse gtt Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | A course in abstract harmonic analysis |
| title_auth | A course in abstract harmonic analysis |
| title_exact_search | A course in abstract harmonic analysis |
| title_full | A course in abstract harmonic analysis Gerald B. Folland |
| title_fullStr | A course in abstract harmonic analysis Gerald B. Folland |
| title_full_unstemmed | A course in abstract harmonic analysis Gerald B. Folland |
| title_short | A course in abstract harmonic analysis |
| title_sort | a course in abstract harmonic analysis |
| topic | Analyse harmonique Analyse harmonique ram Harmonische analyse gtt Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Analyse harmonique Harmonische analyse Harmonic analysis Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007321292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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