Harmonic analysis of functions of several complex variables in the classical domains:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1986
|
| Ausgabe: | reprint. |
| Schriftenreihe: | Translations of mathematical monographs
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. - Orig.-Text in Chines. ersch. |
| Beschreibung: | IV, 164 S. |
| ISBN: | 9780821815564 |
Internformat
MARC
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| 240 | 1 | 0 | |a Garmoniceskij analiz funkcij mnogich kompleksnych peremennych v klassiceskich oblastjach |
| 245 | 1 | 0 | |a Harmonic analysis of functions of several complex variables in the classical domains |c by L. K. Hua |
| 250 | |a reprint. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1986 | |
| 300 | |a IV, 164 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 6 | |
| 500 | |a Aus dem Russ. übers. - Orig.-Text in Chines. ersch. | ||
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere Variable |0 (DE-588)4277015-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Translations of mathematical monographs |v 6 |w (DE-604)BV000002394 |9 6 | |
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Datensatz im Suchindex
| _version_ | 1804140732495167488 |
|---|---|
| adam_text | CONTENTS
Editor s foreword
1
Foreword
З
Introduction
5
I. Classical domains
5
II. Characteristic manifolds
6
III. Heuristic considerations
7
IV. Remarks on the methods to be used
9
V. Applications to representation theory
12
Chapter I. Algebraic machinery
15
1.1.
Algebraic identities
15
1.2.
Power series identities
22
1.3.
Identities for
N(/1, ···./») 29
1.4.
Identities for characters
31
Chapter II. Evaluation of some integrals
33
2.1.
Matrix analogues of the integral
/+.*(1+ϊ2)* ώ
33
2.2.
The volume of
Sai
40
2.3.
The volume of
9Î
π
43
2.4.
The volume of
91
ш
46
2.5.
The volume of
Ж
iv 48
Chapter III. Polar coordinates for matrices
52
3.1.
The volume element of the space of unitary matrices
52
3.2.
Integrals on a coset space ofthe unitary group
55
3.3.
Polar coordinates for hermitian matrices
57
3.4.
Polar coordinates for arbitrary square matrices
58
3.5.
Polar coordinates for symmetric matrices
63
3.6.
Polar coordinates for skew-symmetric matrices
67
3.7.
The volume of the space of real orthogonal matrices and applications
72
Chapter IV. Some general theorems and their applications
77
4.1.
Introduction
77
4.2.
The Bergman kernel
79
4.3.
Bergman kernels for the domains 9t
1, 91
η
and
9Î
ш
83
4.4.
The Bergman kernel for the domain
3Í
iv 85
4.5.
The Cauchy kernel
88
ÍV
CONTENTS
4.6.
The Cauchy formula
90
4.7.
The Cauchy kernels for classical domains
93
4.8.
The
Poisson
kernel for circular domains
97
Chapter V. Harmonic analysis in the space of rectangular matrices
100
5.1.
Orthogonal systems in the space of rectangular matrices
100
5.2.
Integrals of functions which are invariant under the transforma¬
tions Z-iTZT 1
103
5.3.
The orthogonal system and the Bergman kernel
109
5.4.
Harmonic analysis on the characteristic manifold
110
5.5.
Integrals of Cauchy type
113
5.6.
Differential operators
116
5.7.
The meaning ofthe Laplace operator on the boundary of $Ri
118
5.8.
The behavior of the
Poisson
integral on the boundary of 5R
ι
120
5.9.
The solution of Dirichlet e problem in
5И
ι
124
5.10.
A basis for harmonic functions
126
5.11.
Abelian summability of Fourier series on the unitary group
127
Chapter VI. Harmonic analysis in the space of symmetric and
skew-symmetric matrices
130
6.1.
Orthonormal
systems in the space of symmetric unitary matrices
130
6.2.
Projection of a kernel into a subspace
131
6.3.
An
orthonormal
system on
9Î
π
136
6.4.
Characteristic manifold of the space of skew-symmetric matrices
137
Chapter
VII.
Harmonic analysis on Lie spheres
139
7.1. Gegenbauer
polynomials
139
7.2.
Harmonic analysis on the sphere
142
7.3.
Projection of a kernel into a subspace
144
7.4.
Orthonormal
systems on <S
iv 147
7.5.
A complete orthonormal system in
ÍR
iv 148
7.6.
Reduction of a multiple integral to a simple one
151
7.7.
Another form of the expression
(7.6.3) 154
7.8.
Proof of formula
(7.7.5) 155
Appendix
1.
Some equalities
161
Appendix
2.
Coordinates transformation formulas for matrices
167
Appendix
3.
Harmonic analysis on unitary groups
171
Bibliography
183
|
| any_adam_object | 1 |
| author | Hua, Luogeng 1910-1985 |
| author_GND | (DE-588)119001500 |
| author_facet | Hua, Luogeng 1910-1985 |
| author_role | aut |
| author_sort | Hua, Luogeng 1910-1985 |
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| building | Verbundindex |
| bvnumber | BV035791511 |
| classification_rvk | QH 150 SK 780 |
| ctrlnum | (OCoLC)174663266 (DE-599)BVBBV035791511 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | reprint. |
| format | Book |
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| id | DE-604.BV035791511 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:04:39Z |
| institution | BVB |
| isbn | 9780821815564 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018650841 |
| oclc_num | 174663266 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | IV, 164 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Hua, Luogeng 1910-1985 Verfasser (DE-588)119001500 aut Garmoniceskij analiz funkcij mnogich kompleksnych peremennych v klassiceskich oblastjach Harmonic analysis of functions of several complex variables in the classical domains by L. K. Hua reprint. Providence, RI American Math. Soc. 1986 IV, 164 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 6 Aus dem Russ. übers. - Orig.-Text in Chines. ersch. Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Translations of mathematical monographs 6 (DE-604)BV000002394 6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hua, Luogeng 1910-1985 Harmonic analysis of functions of several complex variables in the classical domains Translations of mathematical monographs Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4277015-4 (DE-588)4023453-8 |
| title | Harmonic analysis of functions of several complex variables in the classical domains |
| title_alt | Garmoniceskij analiz funkcij mnogich kompleksnych peremennych v klassiceskich oblastjach |
| title_auth | Harmonic analysis of functions of several complex variables in the classical domains |
| title_exact_search | Harmonic analysis of functions of several complex variables in the classical domains |
| title_full | Harmonic analysis of functions of several complex variables in the classical domains by L. K. Hua |
| title_fullStr | Harmonic analysis of functions of several complex variables in the classical domains by L. K. Hua |
| title_full_unstemmed | Harmonic analysis of functions of several complex variables in the classical domains by L. K. Hua |
| title_short | Harmonic analysis of functions of several complex variables in the classical domains |
| title_sort | harmonic analysis of functions of several complex variables in the classical domains |
| topic | Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Funktionentheorie Mehrere Variable Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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