Harmonic analysis on commutative spaces:
This book starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces. Those spaces form a simultaneous generalization of compact groups, lo...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2007
|
| Series: | Mathematical surveys and monographs
142 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This book starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces. Those spaces form a simultaneous generalization of compact groups, locally compact abelian groups, and riemannian symmetric spaces. Their geometry and function theory is an increasingly active topic in mathematical research, and this book brings the reader up to the frontiers of that research area with the recent classifications of weakly symmetric spaces and of Gelfand pairs. |
| Item Description: | Includes bibliographical references (p. 367-372) and indexes |
| Physical Description: | XV, 387 S. graph. Darst. 27 cm |
| ISBN: | 0821842897 9780821842898 |
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| 100 | 1 | |a Wolf, Joseph Albert |d 1936-2023 |e Verfasser |0 (DE-588)13068130X |4 aut | |
| 245 | 1 | 0 | |a Harmonic analysis on commutative spaces |c Joseph A. Wolf |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2007 | |
| 300 | |a XV, 387 S. |b graph. Darst. |c 27 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 142 | |
| 500 | |a Includes bibliographical references (p. 367-372) and indexes | ||
| 520 | 3 | |a This book starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces. Those spaces form a simultaneous generalization of compact groups, locally compact abelian groups, and riemannian symmetric spaces. Their geometry and function theory is an increasingly active topic in mathematical research, and this book brings the reader up to the frontiers of that research area with the recent classifications of weakly symmetric spaces and of Gelfand pairs. | |
| 650 | 7 | |a Abelse subgroepen |2 gtt | |
| 650 | 4 | |a Analyse harmonique | |
| 650 | 7 | |a Differentiaalmeetkunde |2 gtt | |
| 650 | 4 | |a Espaces algébriques | |
| 650 | 4 | |a Groupes abéliens | |
| 650 | 4 | |a Groupes topologiques | |
| 650 | 4 | |a Géométrie différentielle | |
| 650 | 7 | |a Harmonische analyse |2 gtt | |
| 650 | 7 | |a Ruimten (wiskunde) |2 gtt | |
| 650 | 7 | |a Topologische groepen |2 gtt | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Topological groups | |
| 650 | 4 | |a Abelian groups | |
| 650 | 4 | |a Algebraic spaces | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologische Gruppe |0 (DE-588)4135793-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraischer Raum |0 (DE-588)4141854-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | 1 | |a Topologische Gruppe |0 (DE-588)4135793-0 |D s |
| 689 | 0 | 2 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | 3 | |a Algebraischer Raum |0 (DE-588)4141854-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1369-9 |
| 830 | 0 | |a Mathematical surveys and monographs |v 142 |w (DE-604)BV000018014 |9 142 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016256577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016256577 | ||
Record in the Search Index
| _version_ | 1804137287162789888 |
|---|---|
| adam_text | Contents
Introduction
xiii
Acknowledgments
xv
Notational Conventions
xv
Part
1.
General Theory of Topological Groups
Chapter
1.
Basic Topological Group Theory
3
1.1.
Definition and Separation Properties
3
1.2.
Subgroups, Quotient Groups, and Quotient Spaces
4
1.3.
Connectedness
5
1.4.
Covering Groups
7
1.5.
Transformation Groups and Homogeneous Spaces
8
1.6.
The Locally Compact Case
9
1.7.
Product Groups
12
1.8.
Invariant Metrics on Topological Groups
15
Chapter
2.
Some Examples
19
2.1.
General and Special Linear Groups
19
2.2.
Linear Lie Groups
20
2.3.
Groups Defined by Bilinear Forms
21
2.4.
Groups Defined by Hermitian Forms
22
2.5.
Degenerate Forms
25
2.6.
Automorphism Groups of Algebras
26
2.7.
Spheres,
Projective
Spaces and Grassmannians
28
2.8.
Complexification of Real Groups
30
2.9.
p-adic Groups
32
2.10. Heisenberg
Groups
33
Chapter
3.
Integration and Convolution
35
3.1.
Definition and Examples
35
3.2.
Existence and Uniqueness of
Haar
Measure
36
3.3.
The Modular Function
41
3.4.
Integration on Homogeneous Spaces
44
3.5.
Convolution and the Lebesgue Spaces
45
CONTENTS
Vlil
3.6.
The Group Algebra
3.7.
The Measure Algebra
51
3.8.
Adèle
Groups
Part
2.
Representation Theory and Compact Groups
Chapter
4.
Basic Representation Theory 55
4.1.
Definitions and Examples 56
4.2.
Subrepresentations and Quotient Representations
59
4.3.
Operations on Representations
64
4.3A. Dual Space
64
4.3B. Direct Sum
64
4.3C. Tensor Product of Spaces
65
4.3D. Horn 67
4.3E. Bilinear Forms
6?
4.3F. Tensor Products of Algebras
68
4.3G. Relation with the Commuting Algebra
69
4.4.
Multiplicities and the Commuting Algebra
70
4.5.
Completely Continuous Representations
72
4.6.
Continuous Direct Sums of Representations
75
4.7.
Induced Representations
77
4.8.
Vector Bundle Interpretation
81
4.9.
Mackey s Little-Group Theorem
82
4.9A. The Normal Subgroup Case
82
4.9B. Cohomology and
Projective
Representations
84
4.9C. Cocycle Representations and Extensions
85
4.10.
Mackey Theory and the
Heisenberg
Group
87
Chapter
5.
Representations of Compact Groups
93
5.1.
Finite Dimensionality
93
5.2.
Orthogonality Relations
96
5.3.
Characters and Projections
97
5.4.
The Peter-Weyl Theorem
99
5.5.
The Plancherel Formula
101
5.6.
Decomposition into
Irreducibles
104
5.7.
Some Basic Examples IO7
5.7A. The Group U{1) IO7
5.7B. The Group SU(2) IO7
5.7C. The Group SO(3) 110
5.7D. The Group
50(4)
щ
5.7E. The Sphere S2
ш
5.7F. The Sphere S3
ш
5.8.
Real, Complex and Quaternion Representations
ИЗ
5.9.
The Frobenius Reciprocity Theorem
П5
CONTENTS
Chapter
6.
Compact Lie Groups and Homogeneous Spaces
119
6.1.
Some Generalities on Lie Groups
119
6.2.
Reductive Lie Groups and Lie Algebras
122
6.3.
Cartan s Highest Weight Theory
127
6.4.
The Peter-Weyl Theorem and the Plancherel Formula
131
6.5.
Complex Flag Manifolds and Holomorphic Vector Bundles
133
6.6.
Invariant Function Algebras
136
Chapter
7.
Discrete Co-Compact Subgroups
141
7.1.
Basic Properties of Discrete Subgroups
141
7.2.
Regular Representations on Compact Quotients
146
7.3.
The First Trace Formula for Compact Quotients
147
7.4.
The Lie Group Case
148
Part
3.
Introduction to Commutative Spaces
Chapter
8.
Basic Theory of Commutative Spaces
153
8.1.
Preliminaries
153
8.2.
Spherical Measures and Spherical Functions
156
8.3.
Alternate Formulation in the Differentiable Setting
160
8.4.
Positive Definite Functions
165
8.5.
Induced Spherical Functions
168
8.6.
Example: Spherical Principal Series Representations
170
8.7.
Example: Double Transitivity and Homogeneous Trees
174
8.7A. Doubly Transitive Groups
174
8.7B. Homogeneous Trees
175
8.7C. A Special Case
176
Chapter
9.
Spherical Transforms and Plancherel Formulae
179
9.1.
Commutative Banach Algebras
179
9.2.
The Spherical Transform
184
9.3.
Bochner s Theorem
187
9.4.
The Inverse Spherical Transform
191
9.5.
The Plancherel Formula for K G/K
192
9.6.
The Plancherel Formula for G/K
194
9.7.
The Multiplicity Free Criterion
197
9.8.
Characterizations of Commutative Spaces
198
9.9.
The Uncertainty Principle
199
9.9A. Operator Norm Inequalities for KXG/K
199
9.9B. The Uncertainty Principle for K G/K
202
9.9C. Operator Norm Inequalities for G/K
203
9.9D. The Uncertainty Principle for G/K
204
9.10.
The Compact Case 204
CONTENTS
χ
2Ω7
Chapter
10.
Special Case: Commutative Groups
207
10.1.
The Character Group
10 2
The Fourier Transform and Fourier Inversion Theorems
212
214
10.3.
Pontrjagin Duality
10.4.
Almost Periodic Functions
10.5.
Spectral Theorems
910,
10.6.
The Lie Group Case Ziy
Part
4.
Structure and Analysis for Commutative Spaces
Chapter
11.
Riemannian Symmetric Spaces
225
11.1.
A Fast Tour of Symmetric Space Theory
225
11.
1A. Riemannian Basics
225
11.1
В
.
Lie Theoretic Basics
226
11.1С.
Complex and Quatemionic Structures
229
11.2.
Classifications of Symmetric Spaces
231
11.3.
Euclidean Space
236
11.
ЗА.
Construction of Spherical Functions
236
11.3B. General Spherical Functions on Euclidean Space
238
11.
3C. Positive Definite Spherical Functions on Euclidean
Space
240
11.3D. The Transitive Case
242
11.4.
Symmetric Spaces of Compact Type
245
И.4А.
Restricted Root Systems
245
11.
4B. The Cartan-Helgason Theorem
246
11.
4C. Example: Group Manifolds
249
11.
4D. Examples: Spheres and
Projective
Spaces
250
11.5.
Symmetric Spaces of Noncompact Type
252
11.
5A. Restricted Root Systems
253
11.
5B. Harish-Chandra s Parameterization
254
11.5C. Hyperbolic Spaces
255
11.
5D. The c-Function and Plancherel Measure
257
11.
5E. Example: Groups with Only One Conjugacy Class of
Cartan Subgroups
258
11.6.
Appendix: Finsler Symmetric Spaces
260
Chapter
12.
Weakly Symmetric and Reductive Commutative Spaces
263
12.1.
Commutativity Criteria
263
12.2.
Geometry of Weakly Symmetric Spaces
264
12.3.
Example: Circle Bundles over Hermitian Symmetric Spaces
268
12.4.
Structure of Spherical Spaces
272
12.5.
Complex Weakly Symmetric Spaces
275
12.6.
Spherical Spaces are Weakly Symmetric
277
12.7. Krämer
Classification and the Akhiezer-Vinberg Theorem
282
12.8. Semisimple
Commutative Spaces
287
CONTENTS xi
12.9.
Examples of Passage from the
Semisimple
Case
290
12.10.
Reductive Commutative Spaces
293
Chapter
13.
Structure of Commutative Nilmanifolds
299
13.1.
The 2-step
Nilpotent
Theorem
299
13.1
A. Solvable and
Nilpotent
Radicals
299
13.
IB. Group Theory Proof
300
13.1С.
Digression: Riemannian Geometry Proof
301
13.2.
The Case Where
Λ
is
a
Heisenberg
Group
303
13.3.
The Chevalley-
Vinberg
Decomposition
309
13.
ЗА.
Digression: Chevalley Decompositions
309
13.
3B. Weakly Commutative Spaces
314
13.3C. Weakly Commutative Nilmanifolds
317
13.3D. Vinberg s Decomposition
318
13.4.
Irreducible Commutative Nilmanifolds
319
13.4A. The Irreducible Case
—
Classification
320
13.4B. The Irreducible Case
—
Structure
321
13.
4C. Decomposition into Irreducible Factors
326
13.4D. A Restricted Classification
327
Chapter
14.
Analysis on Commutative Nilmanifolds
329
14.1.
Kirillov Theory
329
14.2.
Moore-Wolf Theory
330
14.3.
The Case where
N
is a (very) Generalized
Heisenberg
Group
335
14.4.
Specialization to Commutative Nilmanifolds
338
14.5.
Spherical Functions
341
14.5A. General Setting for Semidirect Products
N »
К
342
14.5B. The Commutative Nihnanifold Case
342
Chapter
15.
Classification of Commutative Spaces
345
15.1.
The Classification Criterion
345
15.2.
Trees and Forests
350
15.2A. Trees and Triples
350
15.2B. The Mixed Case
351
15.2C. The Nihnanifold Case
353
15.3.
Centers
354
15.4.
Weakly Symmetric Spaces
357
Bibliography
367
Subject Index
373
Symbol Index
383
Table Index
387
|
| adam_txt |
Contents
Introduction
xiii
Acknowledgments
xv
Notational Conventions
xv
Part
1.
General Theory of Topological Groups
Chapter
1.
Basic Topological Group Theory
3
1.1.
Definition and Separation Properties
3
1.2.
Subgroups, Quotient Groups, and Quotient Spaces
4
1.3.
Connectedness
5
1.4.
Covering Groups
7
1.5.
Transformation Groups and Homogeneous Spaces
8
1.6.
The Locally Compact Case
9
1.7.
Product Groups
12
1.8.
Invariant Metrics on Topological Groups
15
Chapter
2.
Some Examples
19
2.1.
General and Special Linear Groups
19
2.2.
Linear Lie Groups
20
2.3.
Groups Defined by Bilinear Forms
21
2.4.
Groups Defined by Hermitian Forms
22
2.5.
Degenerate Forms
25
2.6.
Automorphism Groups of Algebras
26
2.7.
Spheres,
Projective
Spaces and Grassmannians
28
2.8.
Complexification of Real Groups
30
2.9.
p-adic Groups
32
2.10. Heisenberg
Groups
33
Chapter
3.
Integration and Convolution
35
3.1.
Definition and Examples
35
3.2.
Existence and Uniqueness of
Haar
Measure
36
3.3.
The Modular Function
41
3.4.
Integration on Homogeneous Spaces
44
3.5.
Convolution and the Lebesgue Spaces
45
CONTENTS
Vlil
3.6.
The Group Algebra
3.7.
The Measure Algebra
51
3.8.
Adèle
Groups
Part
2.
Representation Theory and Compact Groups
Chapter
4.
Basic Representation Theory 55
4.1.
Definitions and Examples 56
4.2.
Subrepresentations and Quotient Representations
59
4.3.
Operations on Representations
64
4.3A. Dual Space
64
4.3B. Direct Sum
64
4.3C. Tensor Product of Spaces
65
4.3D. Horn 67
4.3E. Bilinear Forms
6?
4.3F. Tensor Products of Algebras
68
4.3G. Relation with the Commuting Algebra
69
4.4.
Multiplicities and the Commuting Algebra
70
4.5.
Completely Continuous Representations
72
4.6.
Continuous Direct Sums of Representations
75
4.7.
Induced Representations
77
4.8.
Vector Bundle Interpretation
81
4.9.
Mackey's Little-Group Theorem
82
4.9A. The Normal Subgroup Case
82
4.9B. Cohomology and
Projective
Representations
84
4.9C. Cocycle Representations and Extensions
85
4.10.
Mackey Theory and the
Heisenberg
Group
87
Chapter
5.
Representations of Compact Groups
93
5.1.
Finite Dimensionality
93
5.2.
Orthogonality Relations
96
5.3.
Characters and Projections
97
5.4.
The Peter-Weyl Theorem
99
5.5.
The Plancherel Formula
101
5.6.
Decomposition into
Irreducibles
104
5.7.
Some Basic Examples IO7
5.7A. The Group U{1) IO7
5.7B. The Group SU(2) IO7
5.7C. The Group SO(3) 110
5.7D. The Group
50(4)
щ
5.7E. The Sphere S2
ш
5.7F. The Sphere S3
ш
5.8.
Real, Complex and Quaternion Representations
ИЗ
5.9.
The Frobenius Reciprocity Theorem
П5
CONTENTS
Chapter
6.
Compact Lie Groups and Homogeneous Spaces
119
6.1.
Some Generalities on Lie Groups
119
6.2.
Reductive Lie Groups and Lie Algebras
122
6.3.
Cartan's Highest Weight Theory
127
6.4.
The Peter-Weyl Theorem and the Plancherel Formula
131
6.5.
Complex Flag Manifolds and Holomorphic Vector Bundles
133
6.6.
Invariant Function Algebras
136
Chapter
7.
Discrete Co-Compact Subgroups
141
7.1.
Basic Properties of Discrete Subgroups
141
7.2.
Regular Representations on Compact Quotients
146
7.3.
The First Trace Formula for Compact Quotients
147
7.4.
The Lie Group Case
148
Part
3.
Introduction to Commutative Spaces
Chapter
8.
Basic Theory of Commutative Spaces
153
8.1.
Preliminaries
153
8.2.
Spherical Measures and Spherical Functions
156
8.3.
Alternate Formulation in the Differentiable Setting
160
8.4.
Positive Definite Functions
165
8.5.
Induced Spherical Functions
168
8.6.
Example: Spherical Principal Series Representations
170
8.7.
Example: Double Transitivity and Homogeneous Trees
174
8.7A. Doubly Transitive Groups
174
8.7B. Homogeneous Trees
175
8.7C. A Special Case
176
Chapter
9.
Spherical Transforms and Plancherel Formulae
179
9.1.
Commutative Banach Algebras
179
9.2.
The Spherical Transform
184
9.3.
Bochner's Theorem
187
9.4.
The Inverse Spherical Transform
191
9.5.
The Plancherel Formula for K\G/K
192
9.6.
The Plancherel Formula for G/K
194
9.7.
The Multiplicity Free Criterion
197
9.8.
Characterizations of Commutative Spaces
198
9.9.
The Uncertainty Principle
199
9.9A. Operator Norm Inequalities for KXG/K
199
9.9B. The Uncertainty Principle for K\G/K
202
9.9C. Operator Norm Inequalities for G/K
203
9.9D. The Uncertainty Principle for G/K
204
9.10.
The Compact Case 204
CONTENTS
χ
2Ω7
Chapter
10.
Special Case: Commutative Groups
207
10.1.
The Character Group
10 2
The Fourier Transform and Fourier Inversion Theorems
212
214
10.3.
Pontrjagin Duality
10.4.
Almost Periodic Functions
10.5.
Spectral Theorems
910,
10.6.
The Lie Group Case Ziy
Part
4.
Structure and Analysis for Commutative Spaces
Chapter
11.
Riemannian Symmetric Spaces
225
11.1.
A Fast Tour of Symmetric Space Theory
225
11.
1A. Riemannian Basics
225
11.1
В
.
Lie Theoretic Basics
226
11.1С.
Complex and Quatemionic Structures
229
11.2.
Classifications of Symmetric Spaces
231
11.3.
Euclidean Space
236
11.
ЗА.
Construction of Spherical Functions
236
11.3B. General Spherical Functions on Euclidean Space
238
11.
3C. Positive Definite Spherical Functions on Euclidean
Space
240
11.3D. The Transitive Case
242
11.4.
Symmetric Spaces of Compact Type
245
И.4А.
Restricted Root Systems
245
11.
4B. The Cartan-Helgason Theorem
246
11.
4C. Example: Group Manifolds
249
11.
4D. Examples: Spheres and
Projective
Spaces
250
11.5.
Symmetric Spaces of Noncompact Type
252
11.
5A. Restricted Root Systems
253
11.
5B. Harish-Chandra's Parameterization
254
11.5C. Hyperbolic Spaces
255
11.
5D. The c-Function and Plancherel Measure
257
11.
5E. Example: Groups with Only One Conjugacy Class of
Cartan Subgroups
258
11.6.
Appendix: Finsler Symmetric Spaces
260
Chapter
12.
Weakly Symmetric and Reductive Commutative Spaces
263
12.1.
Commutativity Criteria
263
12.2.
Geometry of Weakly Symmetric Spaces
264
12.3.
Example: Circle Bundles over Hermitian Symmetric Spaces
268
12.4.
Structure of Spherical Spaces
272
12.5.
Complex Weakly Symmetric Spaces
275
12.6.
Spherical Spaces are Weakly Symmetric
277
12.7. Krämer
Classification and the Akhiezer-Vinberg Theorem
282
12.8. Semisimple
Commutative Spaces
287
CONTENTS xi
12.9.
Examples of Passage from the
Semisimple
Case
290
12.10.
Reductive Commutative Spaces
293
Chapter
13.
Structure of Commutative Nilmanifolds
299
13.1.
The "2-step
Nilpotent"
Theorem
299
13.1
A. Solvable and
Nilpotent
Radicals
299
13.
IB. Group Theory Proof
300
13.1С.
Digression: Riemannian Geometry Proof
301
13.2.
The Case Where
Λ"
is
a
Heisenberg
Group
303
13.3.
The Chevalley-
Vinberg
Decomposition
309
13.
ЗА.
Digression: Chevalley Decompositions
309
13.
3B. Weakly Commutative Spaces
314
13.3C. Weakly Commutative Nilmanifolds
317
13.3D. Vinberg's Decomposition
318
13.4.
Irreducible Commutative Nilmanifolds
319
13.4A. The Irreducible Case
—
Classification
320
13.4B. The Irreducible Case
—
Structure
321
13.
4C. Decomposition into Irreducible Factors
326
13.4D. A Restricted Classification
327
Chapter
14.
Analysis on Commutative Nilmanifolds
329
14.1.
Kirillov Theory
329
14.2.
Moore-Wolf Theory
330
14.3.
The Case where
N
is a (very) Generalized
Heisenberg
Group
335
14.4.
Specialization to Commutative Nilmanifolds
338
14.5.
Spherical Functions
341
14.5A. General Setting for Semidirect Products
N »
К
342
14.5B. The Commutative Nihnanifold Case
342
Chapter
15.
Classification of Commutative Spaces
345
15.1.
The Classification Criterion
345
15.2.
Trees and Forests
350
15.2A. Trees and Triples
350
15.2B. The Mixed Case
351
15.2C. The Nihnanifold Case
353
15.3.
Centers
354
15.4.
Weakly Symmetric Spaces
357
Bibliography
367
Subject Index
373
Symbol Index
383
Table Index
387 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Wolf, Joseph Albert 1936-2023 |
| author_GND | (DE-588)13068130X |
| author_facet | Wolf, Joseph Albert 1936-2023 |
| author_role | aut |
| author_sort | Wolf, Joseph Albert 1936-2023 |
| author_variant | j a w ja jaw |
| building | Verbundindex |
| bvnumber | BV023053237 |
| callnumber-first | Q - Science |
| callnumber-label | QA403 |
| callnumber-raw | QA403 |
| callnumber-search | QA403 |
| callnumber-sort | QA 3403 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)123955254 (DE-599)BVBBV023053237 |
| 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 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023053237 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:25:33Z |
| indexdate | 2024-07-09T21:09:54Z |
| institution | BVB |
| isbn | 0821842897 9780821842898 |
| language | English |
| lccn | 2007060807 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016256577 |
| oclc_num | 123955254 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-824 DE-188 DE-20 |
| owner_facet | DE-384 DE-703 DE-824 DE-188 DE-20 |
| physical | XV, 387 S. graph. Darst. 27 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Wolf, Joseph Albert 1936-2023 Verfasser (DE-588)13068130X aut Harmonic analysis on commutative spaces Joseph A. Wolf Providence, RI American Math. Soc. 2007 XV, 387 S. graph. Darst. 27 cm txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 142 Includes bibliographical references (p. 367-372) and indexes This book starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces. Those spaces form a simultaneous generalization of compact groups, locally compact abelian groups, and riemannian symmetric spaces. Their geometry and function theory is an increasingly active topic in mathematical research, and this book brings the reader up to the frontiers of that research area with the recent classifications of weakly symmetric spaces and of Gelfand pairs. Abelse subgroepen gtt Analyse harmonique Differentiaalmeetkunde gtt Espaces algébriques Groupes abéliens Groupes topologiques Géométrie différentielle Harmonische analyse gtt Ruimten (wiskunde) gtt Topologische groepen gtt Harmonic analysis Topological groups Abelian groups Algebraic spaces Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Algebraischer Raum (DE-588)4141854-2 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Topologische Gruppe (DE-588)4135793-0 s Differentialgeometrie (DE-588)4012248-7 s Algebraischer Raum (DE-588)4141854-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1369-9 Mathematical surveys and monographs 142 (DE-604)BV000018014 142 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016256577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wolf, Joseph Albert 1936-2023 Harmonic analysis on commutative spaces Mathematical surveys and monographs Abelse subgroepen gtt Analyse harmonique Differentiaalmeetkunde gtt Espaces algébriques Groupes abéliens Groupes topologiques Géométrie différentielle Harmonische analyse gtt Ruimten (wiskunde) gtt Topologische groepen gtt Harmonic analysis Topological groups Abelian groups Algebraic spaces Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Topologische Gruppe (DE-588)4135793-0 gnd Algebraischer Raum (DE-588)4141854-2 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4023453-8 (DE-588)4135793-0 (DE-588)4141854-2 |
| title | Harmonic analysis on commutative spaces |
| title_auth | Harmonic analysis on commutative spaces |
| title_exact_search | Harmonic analysis on commutative spaces |
| title_exact_search_txtP | Harmonic analysis on commutative spaces |
| title_full | Harmonic analysis on commutative spaces Joseph A. Wolf |
| title_fullStr | Harmonic analysis on commutative spaces Joseph A. Wolf |
| title_full_unstemmed | Harmonic analysis on commutative spaces Joseph A. Wolf |
| title_short | Harmonic analysis on commutative spaces |
| title_sort | harmonic analysis on commutative spaces |
| topic | Abelse subgroepen gtt Analyse harmonique Differentiaalmeetkunde gtt Espaces algébriques Groupes abéliens Groupes topologiques Géométrie différentielle Harmonische analyse gtt Ruimten (wiskunde) gtt Topologische groepen gtt Harmonic analysis Topological groups Abelian groups Algebraic spaces Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Harmonische Analyse (DE-588)4023453-8 gnd Topologische Gruppe (DE-588)4135793-0 gnd Algebraischer Raum (DE-588)4141854-2 gnd |
| topic_facet | Abelse subgroepen Analyse harmonique Differentiaalmeetkunde Espaces algébriques Groupes abéliens Groupes topologiques Géométrie différentielle Harmonische analyse Ruimten (wiskunde) Topologische groepen Harmonic analysis Topological groups Abelian groups Algebraic spaces Geometry, Differential Differentialgeometrie Harmonische Analyse Topologische Gruppe Algebraischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016256577&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT wolfjosephalbert harmonicanalysisoncommutativespaces |