Analysis and geometry on complex homogeneous domains:
"A number of important topics in complex analysis and geometry are covered in this introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable th...
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
2000
|
| Series: | Progress in mathematics
185 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "A number of important topics in complex analysis and geometry are covered in this introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials."--BOOK JACKET "This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis or as a self-study resource for newcomers to the field."--BOOK JACKET |
| Physical Description: | XVII, 540 S. graph. Darst. |
| ISBN: | 3764341386 0817641386 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface xi
Part I Function Spaces on Complex Semi groups
by Jacques Faraut 1
Introduction 3
I Hilbert Spaces of Holomorphic Functions 5
1.1 Reproducing kernels 5
1.2 Invariant Hilbert spaces of holomorphic functions . . 15
II Invariant Cones and Complex Semi groups 19
II. 1 Complex semi groups 19
11.2 Invariant cones in a representation space 21
11.3 Invariant cones in a simple Lie algebra 26
III Positive Unitary Representations 33
III. 1 Self adjoint operators 33
III. 2 Unitary representations 38
III.3 Positive unitary representations 41
vi Contents
IV Hilbert Function Spaces on Complex Semi groups 45
IV. 1 Schur orthogonality relations 45
IV.2 The Hardy space of a complex semi group 53
IV.3 The Cauchy Szego kernel and the Poisson kernel . . 59
IV.4 Spectral decomposition of the Hardy space 62
V Hilbert Function Spaces on SX(2, C) 65
V.I Complex Olshanski semi group in SL(2, C) 65
V.2 Irreducible positive unitary representations 67
V.3 Characters and formal dimensions of the represen¬
tations 7Tm 73
V.4 Bi invariant Hilbert spaces of holomorphic functions 76
V.5 The Hardy space 78
V.6 The Bergman space 79
VI Hilbert Function Spaces on a Complex Semi simple
Lie Group 83
VI. 1 Bounded symmetric domains 83
VI.2 Irreducible positive unitary representations 88
VI.3 Characters and formal dimensions 96
VI.4 Bi invariant Hilbert spaces of holomorphic functions 98
References 99
Part II Graded Lie Algebras and Pseudo hermitian
Symmetric Spaces
by Soji Kaneyuki 103
Introduction 105
I Semisimple Graded Lie Algebras 107
1.1 Root theory of real semisimple Lie algebras 107
1.2 Semisimple graded Lie algebras Ill
1.3 Example 116
1.4 Tables 119
II Symmetric R Spaces 127
II. 1 Symmetric R spaces and their noncompact duals . . 127
II.2 Sylvester s law of inertia in simple GLA s 133
Contents vii
II.3 Generalized conformal structures and causal
structures 141
III Pseudo Hermitian Symmetric Spaces 151
III.l Pseudo Hermitian spaces and nonconvex Siegel
domains 151
III. 2 Simple reducible pseudo Hermitian symmetric
spaces 166
References 179
Part III Function Spaces on Bounded
Symmetric Domains
by Adam Kordnyi 183
Introduction 185
I Bergman Kernel and Bergman Metric 187
1.1 Domains in Cn 187
1.2 Bergman kernel, reproducing kernels 188
1.3 The Bergman metric 190
II Symmetric Domains
and Symmetric Spaces 193
II. 1 Basic facts, definitions 193
11.2 Riemannian symmetric spaces 194
11.3 Theory of oiLa s 196
11.4 OiLa s of bounded symmetric domains 197
11.5 Cartan subalgebras 200
III Construction of the Hermitian Symmetric Spaces 203
III.l The Borel imbedding theorem 203
III. 2 The Harish Chandra realization 205
III.3 Remarks on classification 209
IV Structure of Symmetric Domains 211
IV. 1 Restricted root system, boundary orbits 211
IV.2 Decomposition under the Cayley transform 217
viii Contents
V The Weighted Bergman Spaces 225
V.I Analysis on symmetric domains 225
V.2 Decomposition under K 230
V.3 Spaces of holomorphic functions 234
VI Differential Operators 243
VI. 1 Properties of As 243
VI.2 Invariant differential operators on fi 246
VI.3 Further results on D(Q) 248
VI.4 Extending Da to p+ 251
VII Function Spaces 257
VII. 1 The holomorphic discrete series 257
VII.2 Analytic continuation of the holomorphic discrete
series 259
VII.3 Explicit formulas for the inner products 264
VII.4 Z/9—spaces and Bergman type projections 267
VII.5 Some questions of duality 270
VII.6 Further results 274
References 277
Part IV The Heat Kernels of Non Compact
Symmetric Spaces
by Qi keng Lu 283
I Introduction 285
II The Laplace Beltrami Operator in
Various Coordinates 303
III The Integral Transformations 321
IV The Heat Kernel of the Hyperball 7eR(m,n) 337
V The Harmonic Forms on the Complex
Grassmann Manifold 351
VI The Horo hypercircle Coordinate of a Complex
Hyperball 365
Contents ix
VII The Heat Kernel of ft//(m) 381
VIII The Matrix Representation of NIRGSS 393
References 423
Part V Jordan Triple Systems
by Guy Roos 425
Introduction 427
I Polynomial Identities 429
1.1 Definition of Jordan triple systems 429
1.2 Identities of minimal degree 431
1.3 Jordan representations and duality 435
1.4 The fundamental identity of degree 7 440
1.5 The Bergman operator 441
II Jordan Algebras 451
11.1 Jordan algebras arising from a JTS 451
11.2 Identities in a Jordan algebra 452
11.3 The JTS associated to a Jordan algebra 458
III The Quasi inverse 461
111.1 Quasi invertibility in a Jordan algebra 461
111.2 Quasi invertibility in a JTS 466
111.3 Identities for the quasi inverse 469
111.4 Differential equations 470
111.5 Addition formulas 472
IV The Generic Minimal Polynomial 475
FV.l Unital Jordan algebras 475
IV.2 General Jordan algebras 486
IV.3 Jordan triple systems 488
V Tripotents and Peirce Decomposition 497
V.I Tripotent elements 497
V.2 Peirce decomposition 498
V.3 Orthogonality of tripotents 501
V.4 Simultaneous Peirce decomposition 503
x Contents
VI Hermitian Positive JTS 507
VI.l Positivity 507
VI.2 Spectral decomposition 510
VI.3 Automorphisms 518
VI.4 The spectral norm 523
VI.5 Classification of Hermitian positive JTS 525
VII Further Results and Open Problems 529
VII. 1 Schmid decomposition 529
VII.2 Compactification of an hermitian positive JTS . . . 530
VII.3 Projective imbedding 531
VII.4 Volume computations 531
VII.5 Some open problems 534
References 535
Index 537
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| spelling | Analysis and geometry on complex homogeneous domains Jacques Faraut ... Boston ; Basel ; Berlin Birkhäuser 2000 XVII, 540 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 185 "A number of important topics in complex analysis and geometry are covered in this introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials."--BOOK JACKET "This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis or as a self-study resource for newcomers to the field."--BOOK JACKET Analyse mathématique ram Fonctions de plusieurs variables complexes ram Géométrie ram Functions of several complex variables Geometry Mathematical analysis Homogene komplexe Mannigfaltigkeit (DE-588)4320782-0 gnd rswk-swf Homogene komplexe Mannigfaltigkeit (DE-588)4320782-0 s DE-604 Faraut, Jacques 1940- Sonstige (DE-588)108109577 oth Progress in mathematics 185 (DE-604)BV000004120 185 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008911066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Analysis and geometry on complex homogeneous domains Progress in mathematics Analyse mathématique ram Fonctions de plusieurs variables complexes ram Géométrie ram Functions of several complex variables Geometry Mathematical analysis Homogene komplexe Mannigfaltigkeit (DE-588)4320782-0 gnd |
| subject_GND | (DE-588)4320782-0 |
| title | Analysis and geometry on complex homogeneous domains |
| title_auth | Analysis and geometry on complex homogeneous domains |
| title_exact_search | Analysis and geometry on complex homogeneous domains |
| title_full | Analysis and geometry on complex homogeneous domains Jacques Faraut ... |
| title_fullStr | Analysis and geometry on complex homogeneous domains Jacques Faraut ... |
| title_full_unstemmed | Analysis and geometry on complex homogeneous domains Jacques Faraut ... |
| title_short | Analysis and geometry on complex homogeneous domains |
| title_sort | analysis and geometry on complex homogeneous domains |
| topic | Analyse mathématique ram Fonctions de plusieurs variables complexes ram Géométrie ram Functions of several complex variables Geometry Mathematical analysis Homogene komplexe Mannigfaltigkeit (DE-588)4320782-0 gnd |
| topic_facet | Analyse mathématique Fonctions de plusieurs variables complexes Géométrie Functions of several complex variables Geometry Mathematical analysis Homogene komplexe Mannigfaltigkeit |
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