Principles of harmonic analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 333 S. |
| ISBN: | 9780387854687 9780387854694 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035250359 | ||
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| 007 | t | ||
| 008 | 090115s2009 |||| 00||| eng d | ||
| 020 | |a 9780387854687 |9 978-0-387-85468-7 | ||
| 020 | |a 9780387854694 |9 978-0-387-85469-4 | ||
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| 035 | |a (DE-599)BVBBV035250359 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
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| 100 | 1 | |a Deitmar, Anton |d 1960- |e Verfasser |0 (DE-588)103439682X |4 aut | |
| 245 | 1 | 0 | |a Principles of harmonic analysis |c Anton Deitmar ; Siegfried Echterhoff |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XV, 333 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Echterhoff, Siegfried |d 1960- |e Verfasser |0 (DE-588)1072636522 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056016&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017056016 | ||
Datensatz im Suchindex
| _version_ | 1804138529024901120 |
|---|---|
| adam_text | Contents
1 Haar Integration 1
1.1 Topological
Groups
.................... 1
1.2
Locally Compact Groups
................. 6
1.3 Haar
Measure
....................... 8
1.4
The Modular Function
.................. 17
1.5
The Quotient Integral Formula
............. 21
1.6
Convolution
........................ 25
1.7
The Fourier Transform
.................. 29
1.8
Exercises
......................... 30
2
Banach Algebras
33
2.1
Banach Algebras
..................... 33
2.2
The Spectrum
σΑ(α)
................... 37
2.3
Adjoining a Unit
..................... 41
2.4
The Gelfand Map
..................... 43
2.5
Maximal Ideals
...................... 47
2.6
The Gelfand-Naimark Theorem
............. 49
2.7
The Continuous Functional Calculus
.......... 54
2.8
Exercises and Notes
................... 58
3
Duality for Abelian Groups
63
xi
xii
CONTENTS
3.1
The Dual Group
..................... 63
3.2
The Fourier Transform
.................. 67
3.3
The
C-Algebra
of an LCA-Group
........... 69
3.4
The Plancherel Theorem
................. 72
3.5
Pontryagin Duality
.................... 78
3.6
The
Poisson
Summation Formula
............ 83
3.7
Exercises and Notes
................... 86
4
The Structure of LCA-Groups
91
4.1
Connectedness
...................... 91
4.2
The Structure Theorems
................. 95
4.3
Exercises
.........................107
5
Operators on Hubert Spaces
109
5.1
Functional Calculus
...................109
5.2
Compact Operators
...................115
5.3
Hilbert-Schmidt and Trace Class
............119
5.4
Exercises
.........................124
6
Representations
127
6.1
Schur s Lemma
......................127
6.2
Representations of L1 (G)
................131
6.3
Exercises
.........................135
7
Compact Groups
139
7.1
Finite Dimensional Representations
...........139
7.2
The Peter-Weyl Theorem
................141
7.3
Isotypes
..........................145
7.4
Induced Representations
.................148
CONTENTS xiii
7.5
Representations of SU(2)
................150
7.6
Exercises
.........................156
8
Direct Integrals
159
8.1 Von
Neumann Algebras
.................159
8.2
Weak and Strong Topologies
..............160
8.3
Representations
......................162
8.4
Hubert Integrals
.....................165
8.5
The Plancherel Theorem
.................167
8.6
Exercises
.........................169
9
The Selberg Trace Formula
171
9.1
Cocompact Groups and Lattices
............171
9.2
Discreteness of the Spectrum
..............174
9.3
The Trace Formula
....................179
9.4
Locally Constant Functions
...............185
9.5
Exercises and Notes
...................186
10
The
Heisenberg
Group
189
10.1
Definition
.........................189
10.2
The Unitary Dual
....................190
10.3
The Plancherel Theorem for
Я
.............195
10.4
The Standard Lattice
..................196
10.5
Exercises and Notes
...................199
11
SL2(K)
201
11.1
The Upper Half Plane
..................201
11.2
The
Hecke
Algebra
....................205
11.3
An Explicit Plancherel Theorem
............214
xiv
CONTENTS
11.4
The Trace Formula
....................216
11.5
Weyl s Asymptotic Law
.................222
11.6
The Selberg
Zeta
Function
................225
11.7
Exercises and Notes
...................229
12
Wavelets
233
12.1
First Ideas
.........................233
12.2
Discrete Series Representations
.............239
12.3
Examples of Wavelet Transforms
............246
12.4
Exercises and Notes
...................255
A Topology
259
A.I Generators and Countability
..............260
A.2 Continuity
.........................261
A.3 Compact Spaces
.....................262
A.4 Hausdorff Spaces
.....................264
A.
5
Initial- and Final-Topologies
...............265
A.6 Nets
............................267
A.7 Tychonov s Theorem
...................271
A.8 The Lemma of Urysohn
.................273
A.9 Baire Spaces
.......................275
A.1Ü
The Stone-
Weierstraß
Theorem
.............276
В
Measure and Integration
281
B.I Measurable Functions and Integration
.........281
B.2 The Riesz Representation Theorem
...........285
B.3
Fubinľs
Theorem
.....................287
B.4 Lp-Sphces and the Riesz-Fischer
Theorem
..........................291
CONTENTS xv
В.
5
The Radon-Nikodym Theorem
.............296
B.6 Vector-Valued Integrals
.................297
С
Functional Analysis
305
C.I Basic Concepts
......................305
C.2 Seminorms
........................311
C.3 Hilbert Spaces
......................313
C.4 Unbounded Operators
..................316
Bibiliography
323
Index
329
|
| any_adam_object | 1 |
| author | Deitmar, Anton 1960- Echterhoff, Siegfried 1960- |
| author_GND | (DE-588)103439682X (DE-588)1072636522 |
| author_facet | Deitmar, Anton 1960- Echterhoff, Siegfried 1960- |
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| classification_tum | MAT 420f |
| ctrlnum | (OCoLC)277275470 (DE-599)BVBBV035250359 |
| dewey-full | 515.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.2433 |
| dewey-search | 515.2433 |
| dewey-sort | 3515.2433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035250359 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:29:38Z |
| institution | BVB |
| isbn | 9780387854687 9780387854694 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017056016 |
| oclc_num | 277275470 |
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| physical | XV, 333 S. |
| publishDate | 2009 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Deitmar, Anton 1960- Verfasser (DE-588)103439682X aut Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff New York, NY Springer 2009 XV, 333 S. txt rdacontent n rdamedia nc rdacarrier Universitext Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Echterhoff, Siegfried 1960- Verfasser (DE-588)1072636522 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056016&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deitmar, Anton 1960- Echterhoff, Siegfried 1960- Principles of harmonic analysis Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Principles of harmonic analysis |
| title_auth | Principles of harmonic analysis |
| title_exact_search | Principles of harmonic analysis |
| title_full | Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff |
| title_fullStr | Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff |
| title_full_unstemmed | Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff |
| title_short | Principles of harmonic analysis |
| title_sort | principles of harmonic analysis |
| topic | Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonic analysis Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056016&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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