Analysis on Lie groups: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
110 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 302 S. |
| ISBN: | 9780521719308 |
Staff View
MARC
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| 245 | 1 | 0 | |a Analysis on Lie groups |b an introduction |c Jacques Faraut |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a X, 302 S. | ||
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 110 | |
| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
page
ix
1
The
linear
group
1
1.1
Topological groups
1
1.2
The group GL(n, R) 2
1.3
Examples of subgroups of
G
L(n
,
R)
5
1.4
Polar decomposition in GL(n, R)
7
1.5
The orthogonal group H
1.6
Gram decomposition
13
1.7
Exercises
14
2
The exponential map
18
2.1
Exponential of a matrix
18
2.2
Logarithm of a matrix
25
2.3
Exercises
29
3
Linear Lie groups
36
3.1
One parameter subgroups
36
3.2
lie algebra of a linear Lie group
38
3.3
linear lie groups are submanifolds
41
3.4
Campbell-Hausdorff formula
44
3.5
Exercises
47
4
Lie algebras 50
4.1
Definitions and examples
50
4.2 Nilpotent
and solvable Lie algebras
56
4.3
Semi-simple Lie algebras
62
4.4
Exercises
69
vi
Contents
5
Haar
measure
74
5.1
Haar
measure
74
5.2
Case of a group which is an open set in R
76
5.3
Haar
measure on a product
78
5.4
Some facts about differential calculus
81
5.5
Invariant vector fields and
Haar
measure on a linear Lie group
86
5.6
Exercises
90
6
Representations of compact groups
95
6.1
Unitary representations
95
6.2
Compact self-adjoint operators
98
6.3
Schur
orthogonality relations
103
6.4
Peter-Weyl Theorem
107
6.5
Characters and central functions
115
6.6
Absolute convergence of Fourier series
117
6.7
Casimir
operator
119
6.8
Exercises
123
7
The groups
5(7(2)
and S0(3),
Haar
measures
and irreducible representations
127
7.1
Adjoint representation of SU(2)
127
7.2
Haar
measure on
5ř/(2)
130
7.3
The group
50(3)
133
7.4
Euler
angles
134
7.5
Irreducible representations of SU(2)
136
7.6
Irreducible representations of
50(3)
142
7.7
Exercises
149
8
Analysis on the group SU(2)
158
8.1
Fourier series on
50(2)
158
8.2
Functions of class Ck
160
8.3
Laplace operator on the group
SUÇ2)
163
8.4
Uniform convergence of Fourier series on the group SU(2)
167
8.5
Heat equation on
50(2)
172
8.6
Heat equation on
517(2)
176
8.7
Exercises
182
9
Analysis on the sphere and the Euclidean space
186
9.1
Integration formulae
186
9.2
Laplace operator
191
9.3
Spherical harmonics
194
9.4
Spherical polynomials
200
Contents
vii
9.5 Funk-Hecke Theorem 204
9.6
Fourier
transform
and Bochner-Hecke relations
208
9.7
Dirichlet problem and
Poisson
kernel
212
9.8
An integral transform
220
9.9
Heat equation
225
9.10
Exercises
227
10
Analysis on the spaces of symmetric and Hermitian matrices
231
10.1
Integration formulae
231
10.2
Radial part of the Laplace operator
238
10.3
Heat equation and orbital integrals
242
10.4
Fourier transforms of invariant functions
245
10.5
Exercises
246
11
Irreducible representations of the unitary group
249
11.1
Highest weight theorem
249
11.2
Weyl formulae
253
11.3
Holomorphic representations
260
11.4
Polynomial representations
264
11.5
Exercises
269
12
Analysis on the unitary group
274
12.1
Laplace operator
274
12.2
Uniform convergence of Fourier series on the unitary group
276
12.3
Series expansions of central functions
278
12.4
Generalised Taylor series
284
12.5
Radial part of the Laplace operator on the unitary group
288
12.6
Heat equation on the unitary group
292
12.7
Exercises
297
Bibliography
299
Index
301
|
| adam_txt |
Contents
Preface
page
ix
1
The
linear
group
1
1.1
Topological groups
1
1.2
The group GL(n, R) 2
1.3
Examples of subgroups of
G
L(n
,
R)
5
1.4
Polar decomposition in GL(n, R)
7
1.5
The orthogonal group H
1.6
Gram decomposition
13
1.7
Exercises
14
2
The exponential map
18
2.1
Exponential of a matrix
18
2.2
Logarithm of a matrix
25
2.3
Exercises
29
3
Linear Lie groups
36
3.1
One parameter subgroups
36
3.2
lie algebra of a linear Lie group
38
3.3
linear lie groups are submanifolds
41
3.4
Campbell-Hausdorff formula
44
3.5
Exercises
47
4
Lie algebras 50
4.1
Definitions and examples
50
4.2 Nilpotent
and solvable Lie algebras
56
4.3
Semi-simple Lie algebras
62
4.4
Exercises
69
vi
Contents
5
Haar
measure
74
5.1
Haar
measure
74
5.2
Case of a group which is an open set in R"
76
5.3
Haar
measure on a product
78
5.4
Some facts about differential calculus
81
5.5
Invariant vector fields and
Haar
measure on a linear Lie group
86
5.6
Exercises
90
6
Representations of compact groups
95
6.1
Unitary representations
95
6.2
Compact self-adjoint operators
98
6.3
Schur
orthogonality relations
103
6.4
Peter-Weyl Theorem
107
6.5
Characters and central functions
115
6.6
Absolute convergence of Fourier series
117
6.7
Casimir
operator
119
6.8
Exercises
123
7
The groups
5(7(2)
and S0(3),
Haar
measures
and irreducible representations
127
7.1
Adjoint representation of SU(2)
127
7.2
Haar
measure on
5ř/(2)
130
7.3
The group
50(3)
133
7.4
Euler
angles
134
7.5
Irreducible representations of SU(2)
136
7.6
Irreducible representations of
50(3)
142
7.7
Exercises
149
8
Analysis on the group SU(2)
158
8.1
Fourier series on
50(2)
158
8.2
Functions of class Ck
160
8.3
Laplace operator on the group
SUÇ2)
163
8.4
Uniform convergence of Fourier series on the group SU(2)
167
8.5
Heat equation on
50(2)
172
8.6
Heat equation on
517(2)
176
8.7
Exercises
182
9
Analysis on the sphere and the Euclidean space
186
9.1
Integration formulae
186
9.2
Laplace operator
191
9.3
Spherical harmonics
194
9.4
Spherical polynomials
200
Contents
vii
9.5 Funk-Hecke Theorem 204
9.6
Fourier
transform
and Bochner-Hecke relations
208
9.7
Dirichlet problem and
Poisson
kernel
212
9.8
An integral transform
220
9.9
Heat equation
225
9.10
Exercises
227
10
Analysis on the spaces of symmetric and Hermitian matrices
231
10.1
Integration formulae
231
10.2
Radial part of the Laplace operator
238
10.3
Heat equation and orbital integrals
242
10.4
Fourier transforms of invariant functions
245
10.5
Exercises
246
11
Irreducible representations of the unitary group
249
11.1
Highest weight theorem
249
11.2
Weyl formulae
253
11.3
Holomorphic representations
260
11.4
Polynomial representations
264
11.5
Exercises
269
12
Analysis on the unitary group
274
12.1
Laplace operator
274
12.2
Uniform convergence of Fourier series on the unitary group
276
12.3
Series expansions of central functions
278
12.4
Generalised Taylor series
284
12.5
Radial part of the Laplace operator on the unitary group
288
12.6
Heat equation on the unitary group
292
12.7
Exercises
297
Bibliography
299
Index
301 |
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| id | DE-604.BV023324181 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:54:52Z |
| indexdate | 2024-07-09T21:15:53Z |
| institution | BVB |
| isbn | 9780521719308 |
| language | English |
| lccn | 2007053046 |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Faraut, Jacques 1940- Verfasser (DE-588)108109577 aut Analysis on Lie groups an introduction Jacques Faraut 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 X, 302 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 110 Includes bibliographical references and index Lie algebras Lie groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Lie-Gruppe (DE-588)4035695-4 s Analysis (DE-588)4001865-9 s DE-604 Cambridge studies in advanced mathematics 110 (DE-604)BV000003678 110 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016508225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faraut, Jacques 1940- Analysis on Lie groups an introduction Cambridge studies in advanced mathematics Lie algebras Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4001865-9 (DE-588)4151278-9 |
| title | Analysis on Lie groups an introduction |
| title_auth | Analysis on Lie groups an introduction |
| title_exact_search | Analysis on Lie groups an introduction |
| title_exact_search_txtP | Analysis on Lie groups an introduction |
| title_full | Analysis on Lie groups an introduction Jacques Faraut |
| title_fullStr | Analysis on Lie groups an introduction Jacques Faraut |
| title_full_unstemmed | Analysis on Lie groups an introduction Jacques Faraut |
| title_short | Analysis on Lie groups |
| title_sort | analysis on lie groups an introduction |
| title_sub | an introduction |
| topic | Lie algebras Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Lie algebras Lie groups Lie-Gruppe Analysis Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016508225&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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