Holomorphy and convexity in Lie theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin ; New York
<<de>> Gruyter
2000
|
| Schriftenreihe: | De Gruyter expositions in mathematics
28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 751 - 766. - Auch im Internet unter der Adresse http://www.mathematik.tu-darmstadt.de/ags/ag05/professoren/neeb/hacbook.html verfügbar |
| Beschreibung: | XXI, 778 S. graph. Darst. |
| ISBN: | 3110156695 |
Internformat
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| 245 | 1 | 0 | |a Holomorphy and convexity in Lie theory |c by Karl-Hermann Neeb |
| 264 | 1 | |a Berlin ; New York |b <<de>> Gruyter |c 2000 | |
| 300 | |a XXI, 778 S. |b graph. Darst. | ||
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| 490 | 1 | |a De Gruyter expositions in mathematics |v 28 | |
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| 650 | 7 | |a Fonctions convexes |2 ram | |
| 650 | 7 | |a Lie, Groupes de |2 ram | |
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| 650 | 0 | 7 | |a Konvexe Geometrie |0 (DE-588)4407260-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127624281194496 |
|---|---|
| adam_text | Contents
Preface v
Introduction xiii
A. Abstract Representation Theory
Chapter I. Reproducing Kernel Spaces 3
1.1. Operator Valued Positive Definite Kernels 3
1.2. The Cone of Positive Definite Kernels 14
Chapter II. Representations of Involutive Semigroups 20
11.1. Involutive Semigroups 21
11.2. Bounded Representations 24
11.3. Hermitian Representations 29
11.4. Representations on Reproducing Kernel Spaces 34
Chapter III. Positive Definite Functions on Involutive Semigroups 52
111.1. Positive Definite Functions—the Discrete Case 53
111.2. Enveloping C* algebras 68
111.3. Multiplicity Free Representations 80
Chapter IV. Continuous and Holomorphic Representations .... 99
IV. 1. Continuous Representations and Positive Definite Functions .... 99
IV.2. Holomorphic Representations of Involutive Semigroups 119
B. Convex Geometry and Representations of Vector Spaces
Chapter V. Convex Sets and Convex Functions 125
V.I. Convex Sets and Cones 126
V.2. Finite Reflection Groups and Convex Sets 138
V.3. Convex Functions and Fenchel Duality 147
V.4. Laplace Transforms 163
V.5. The Characteristic Function of a Convex Set 174
x Contents
Chapter VI. Representations of Cones and Tubes 184
VI.1. Commutative Representation Theory 185
VI.2. Representations of Cones 195
VI.3. Holomorphic Representations of Tubes 205
VI.4. Realization of Cyclic Representations by Holomorphic Functions . . 209
VI.5. Holomorphic Extensions of Unitary Representations 214
C. Convex Geometry of Lie Algebras
Chapter VII. Convexity in Lie Algebras 221
VII. 1. Compactly Embedded Cartan Subalgebras 222
VII.2. Root Decompositions 231
VII.3. Lie Algebras With Many Invariant Convex Sets 251
Chapter VIII. Convexity Theorems and Their Applications .... 265
VIII.I. Admissible Coadjoint Orbits and Convexity Theorems 266
VIII.2. The Structure of Admissible Lie Algebras 292
VIII.3. Invariant Elliptic Cones in Lie Algebras 306
D. Highest Weight Representations of Lie Algebras,
Lie Groups, and Semigroups
Chapter IX. Unitary Highest Weight Representations:
Algebraic Theory 327
IX. 1. Generalized Highest Weight Representations 328
IX.2. Positive Complex Polarizations 344
IX.3. Highest Weight Modules of Finite Dimensional Lie Algebras . . . 356
IX.4. The Metaplectic Factorization 361
IX.5. Unitary Highest Weight Representations of Hermitian Lie Algebras 374
Chapter X. Unitary Highest Weight Representations:
Analytic Theory 387
X.I. The Convex Moment Set of a Unitary Representation 388
X.2. Irreducible Unitary Representations 394
X.3. The Metaplectic Representation and Its Applications 400
X.4. Special Properties of Unitary Highest Weight Representations . . .411
X.5. Moment Sets for C* algebras 419
X.6. Moment Sets for Group Representations 428
Contents xi
Chapter XI. Complex OFshanskii Semigroups and
Their Representations 442
XI. 1. Lawson s Theorem on Ol shanskii Semigroups 443
XI.2. Holomorphic Extension of Unitary Representations 457
XI.3. Holomorphic Representations of Ol shanskii Semigroups 464
XI.4. Irreducible Holomorphic Representations 470
XI.5. Gelfand Ra ikov Theorems for Ol shanskii Semigroups 476
XI.6. Decomposition and Characters of Holomorphic Representations . . 477
Chapter XII. Realization of Highest Weight Representations
on Complex Domains 493
XII. 1. The Structure of Groups of Harish Chandra Type 494
XII.2. Representations of Groups of Harish Chandra Type 514
XII.3. The Compression Semigroup and Its Representations 524
XII.4. Examples 530
XII.5. Hilbert Spaces of Square Integrable Holomorphic Functions .... 538
E. Complex Geometry and Representation Theory
Chapter XIII. Complex and Convex Geometry
of Complex Semigroups 557
XIII. 1. Locally Convex Functions and Local Recession Cones 559
XIII.2. Invariant Convex Sets and Functions in Lie Algebras 563
XIII.3. Calculations in Low Dimensional Cases 571
XIII.4. Biinvariant Plurisubharmonic Functions 576
XIII.5. Complex Semigroups and Stein Manifolds 586
XIII.6. Biinvariant Domains of Holomorphy 595
Chapter XIV. Biinvariant Hilbert Spaces and Hardy Spaces
on Complex Semigroups 600
XIV.l. Biinvariant Hilbert Spaces 601
XIV.2. Hardy Spaces Defined by Sup Norms 608
XIV.3. Hardy Spaces Defined by Square Integrability 616
XIV.4. The Fine Structure of Hardy Spaces 623
Chapter XV. Coherent State Representations 645
XV. 1. Complex Structures on Homogeneous Spaces 646
XV.2. Coherent State Representations 650
XV.3. Heisenberg s Uncertainty Principle and Coherent States 656
xii Contents
Appendices
Appendix I. Bounded Operators on Hilbert Spaces 665
Appendix II. Spectral Measures and Unbounded Operators 677
Appendix III. Holomorphic Functions on Infinite Dimensional Spaces . . 686
Appendix IV. Symplectic Geometry 694
Appendix V. Simple Modules of p Length 2 705
Appendix VI. Symplectic Modules of Convex Type 715
Appendix VII. Square Integrable Representations of Locally
Compact Groups 727
Appendix VIII. The Stone von Neumann Mackey Theorem 742
Bibliography 751
List of Symbols 767
Index 771
|
| any_adam_object | 1 |
| author | Neeb, Karl-Hermann 1964- |
| author_GND | (DE-588)112163920 |
| author_facet | Neeb, Karl-Hermann 1964- |
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| classification_rvk | SK 340 |
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| dewey-full | 512.2 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 512.55 |
| dewey-search | 512.2 512.55 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012932784 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:36:18Z |
| institution | BVB |
| isbn | 3110156695 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008806100 |
| oclc_num | 468518906 |
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| owner_facet | DE-824 DE-355 DE-BY-UBR DE-20 DE-11 DE-29T |
| physical | XXI, 778 S. graph. Darst. |
| publishDate | 2000 |
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| publishDateSort | 2000 |
| publisher | <<de>> Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Neeb, Karl-Hermann 1964- Verfasser (DE-588)112163920 aut Holomorphy and convexity in Lie theory by Karl-Hermann Neeb Berlin ; New York <<de>> Gruyter 2000 XXI, 778 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 28 Literaturverz. S. 751 - 766. - Auch im Internet unter der Adresse http://www.mathematik.tu-darmstadt.de/ags/ag05/professoren/neeb/hacbook.html verfügbar Fonctions convexes ram Lie, Groupes de ram Représentations de groupes ram Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Unitäre Darstellung (DE-588)4186906-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Holomorphe Darstellung (DE-588)4347868-2 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Holomorphe Darstellung (DE-588)4347868-2 s Unitäre Darstellung (DE-588)4186906-0 s Konvexe Geometrie (DE-588)4407260-0 s DE-604 De Gruyter expositions in mathematics 28 (DE-604)BV004069300 28 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008806100&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neeb, Karl-Hermann 1964- Holomorphy and convexity in Lie theory De Gruyter expositions in mathematics Fonctions convexes ram Lie, Groupes de ram Représentations de groupes ram Lie-Algebra (DE-588)4130355-6 gnd Unitäre Darstellung (DE-588)4186906-0 gnd Konvexe Geometrie (DE-588)4407260-0 gnd Holomorphe Darstellung (DE-588)4347868-2 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4186906-0 (DE-588)4407260-0 (DE-588)4347868-2 |
| title | Holomorphy and convexity in Lie theory |
| title_auth | Holomorphy and convexity in Lie theory |
| title_exact_search | Holomorphy and convexity in Lie theory |
| title_full | Holomorphy and convexity in Lie theory by Karl-Hermann Neeb |
| title_fullStr | Holomorphy and convexity in Lie theory by Karl-Hermann Neeb |
| title_full_unstemmed | Holomorphy and convexity in Lie theory by Karl-Hermann Neeb |
| title_short | Holomorphy and convexity in Lie theory |
| title_sort | holomorphy and convexity in lie theory |
| topic | Fonctions convexes ram Lie, Groupes de ram Représentations de groupes ram Lie-Algebra (DE-588)4130355-6 gnd Unitäre Darstellung (DE-588)4186906-0 gnd Konvexe Geometrie (DE-588)4407260-0 gnd Holomorphe Darstellung (DE-588)4347868-2 gnd |
| topic_facet | Fonctions convexes Lie, Groupes de Représentations de groupes Lie-Algebra Unitäre Darstellung Konvexe Geometrie Holomorphe Darstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008806100&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
| work_keys_str_mv | AT neebkarlhermann holomorphyandconvexityinlietheory |