Holomorphy and convexity in Lie theory /:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Walter de Gruyter,
2000.
|
| Schriftenreihe: | De Gruyter expositions in mathematics ;
28. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (xxi, 778 pages) |
| Bibliographie: | Includes bibliographical references (pages 751-766) and index. |
| ISBN: | 9783110808148 3110808145 |
| ISSN: | 0938-6572 ; |
Internformat
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
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| 020 | |a 9783110808148 |q (electronic bk.) | ||
| 020 | |a 3110808145 |q (electronic bk.) | ||
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| 049 | |a MAIN | ||
| 100 | 1 | |a Neeb, Karl-Hermann. | |
| 245 | 1 | 0 | |a Holomorphy and convexity in Lie theory / |c by Karl-Hermann Neeb. |
| 264 | 1 | |a New York : |b Walter de Gruyter, |c 2000. | |
| 300 | |a 1 online resource (xxi, 778 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics, |x 0938-6572 ; |v 28 | |
| 504 | |a Includes bibliographical references (pages 751-766) and index. | ||
| 505 | 0 | 0 | |g A. |t Abstract Representation Theory -- |g Chapter I. |t Reproducing Kernel Spaces |g 3 -- |g I.1. |t Operator-Valued Positive Definite Kernels |g 3 -- |g I.2. |t The Cone of Positive Definite Kernels |g 14 -- |g Chapter II. |t Representations of Involutive Semigroups |g 20 -- |g II. 1. |t Involutive Semigroups |g 21 -- |g II. 2. |t Bounded Representations |g 24 -- |g II. 3. |t Hermitian Representations |g 29 -- |g II. 4. |t Representations on Reproducing Kernel Spaces |g 34 -- |g Chapter III. |t Positive Definite Functions on Involutive Semigroups |g 52 -- |g III. 1. |t Positive Definite Functions -- the Discrete Case |g 53 -- |g III. 2. |t Enveloping C*-algebras |g 68 -- |g III. 3. |t Multiplicity Free Representations |g 80 -- |g Chapter IV. |t Continuous and Holomorphic Representations |g 99 -- |g IV. 1. |t Continuous Representations and Positive Definite Functions |g 99 -- |g IV. 2. |t Holomorphic Representations of Involutive Semigroups |g 119 -- |g B. |t Convex Geometry and Representations of Vector Spaces -- |g Chapter V. |t Convex Sets and Convex Functions |g 125 -- |g V.1. |t Convex Sets and Cones |g 126 -- |g V.2. |t Finite Reflection Groups and Convex Sets |g 138 -- |g V.3. |t Convex Functions and Fenchel Duality |g 147 -- |g V.4. |t Laplace Transforms |g 163 -- |g V.5. |t The Characteristic Function of a Convex Set |g 174 -- |g Chapter VI. |t Representations of Cones and Tubes |g 184 -- |g VI. 1. |t Commutative Representation Theory |g 185 -- |g VI. 2. |t Representations of Cones |g 195 -- |g VI. 3. |t Holomorphic Representations of Tubes |g 205 -- |g VI. 4. |t Realization of Cyclic Representations by Holomorphic Functions |g 209 -- |g VI. 5. |t Holomorphic Extensions of Unitary Representations |g 214 -- |g C. |t Convex Geometry of Lie Algebras -- |g Chapter VII. |t Convexity in Lie Algebras |g 221 -- |g VII. 1. |t Compactly Embedded Cartan Subalgebras |g 222 -- |g VII. 2. |t Root Decompositions |g 231 -- |g VII. 3. |t Lie Algebras With Many Invariant Convex Sets |g 251 -- |g Chapter VIII. |t Convexity Theorems and Their Applications |g 265 -- |g VIII. 1. |t Admissible Coadjoint Orbits and Convexity Theorems |g 266 -- |g VIII. 2. |t The Structure of Admissible Lie Algebras |g 292 -- |g VIII. 3. |t Invariant Elliptic Cones in Lie Algebras |g 306 -- |g D. |t Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups -- |g Chapter IX. |t Unitary Highest Weight Representations: Algebraic Theory |g 327 -- |g IX. 1. |t Generalized Highest Weight Representations |g 328 -- |g IX. 2. |t Positive Complex Polarizations |g 344 -- |g IX. 3. |t Highest Weight Modules of Finite-Dimensional Lie Algebras |g 356 -- |g IX. 4. |t The Metaplectic Factorization |g 361 -- |g IX. 5. |t Unitary Highest Weight Representations of Hermitian Lie Algebras |g 374 -- |g Chapter X. |t Unitary Highest Weight Representations: Analytic Theory |g 387 -- |g X.1. |t The Convex Moment Set of a Unitary Representation |g 388 -- |g X.2. |t Irreducible Unitary Representations |g 394 -- |g X.3. |t The Metaplectic Representation and Its Applications |g 400 -- |g X.4. |t Special Properties of Unitary Highest Weight Representations |g 411 -- |g X.5. |t Moment Sets for C*-algebras |g 419 -- |g X.6. |t Moment Sets for Group Representations |g 428 -- |g Chapter XI. |t Complex Ol'shanskii Semigroups and Their Representations |g 442 -- |g XI. 1. |t Lawson's Theorem on Ol'shanskii Semigroups |g 443 -- |g XI. 2. |t Holomorphic Extension of Unitary Representations |g 457 -- |g XI. 3. |t Holomorphic Representations of Ol'shanskii Semigroups |g 464 -- |g XI. 4. |t Irreducible Holomorphic Representations |g 470 -- |g XI. 5. |t Gelfand-Raikov Theorems for Ol'shanskii Semigroups |g 476 -- |g XI. 6. |t Decomposition and Characters of Holomorphic Representations |g 477 -- |g Chapter XII. |t Realization of Highest Weight Representations on Complex Domains |g 493 -- |g XII. 1. |t The Structure of Groups of Harish-Chandra Type |g 494 -- |g XII. 2. |t Representations of Groups of Harish-Chandra Type |g 514 -- |g XII. 3. |t The Compression Semigroup and Its Representations |g 524 -- |g XII. 5. |t Hilbert Spaces of Square Integrable Holomorphic Functions |g 538 -- |g E. |t Complex Geometry and Representation Theory -- |g Chapter XIII. |t Complex and Convex Geometry of Complex Semigroups |g 557 -- |g XIII. 1. |t Locally Convex Functions and Local Recession Cones |g 559 -- |g XIII. 2. |t Invariant Convex Sets and Functions in Lie Algebras |g 563 -- |g XIII. 3. |t Calculations in Low-Dimensional Cases |g 571 -- |g XIII. 4. |t Biinvariant Plurisubharmonic Functions |g 576 -- |g XIII. 5. |t Complex Semigroups and Stein Manifolds |g 586 -- |g XIII. 6. |t Biinvariant Domains of Holomorphy |g 595 -- |g Chapter XIV. |t Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups |g 600 -- |g XIV. 1. |t Biinvariant Hilbert Spaces |g 601 -- |g XIV. 2. |t Hardy Spaces Defined by Sup-Norms |g 608 -- |g XIV. 3. |t Hardy Spaces Defined by Square Integrability |g 616 -- |g XIV. 4. |t The Fine Structure of Hardy Spaces |g 623 -- |g Chapter XV. |t Coherent State Representations |g 645 -- |g XV. 1. |t Complex Structures on Homogeneous Spaces |g 646 -- |g XV. 2. |t Coherent State Representations |g 650 -- |g XV. 3. |t Heisenberg's Uncertainty Principle and Coherent States |g 656 -- |g Appendix I. |t Bounded Operators on Hilbert Spaces |g 665 -- |g Appendix II. |t Spectral Measures and Unbounded Operators |g 677 -- |g Appendix III. |t Holomorphic Functions on Infinite-Dimensional Spaces |g 686 -- |g Appendix IV. |t Symplectic Geometry |g 694 -- |g Appendix V. |t Simple Modules of p-Length 2 |g 705 -- |g Appendix VI. |t Symplectic Modules of Convex Type |g 715 -- |g Appendix VII. |t Square Integrable Representations of Locally Compact Groups |g 727 -- |g Appendix VIII. |t The Stone-von Neumann-Mackey Theorem |g 742. |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Lie groups. |0 http://id.loc.gov/authorities/subjects/sh85076786 | |
| 650 | 0 | |a Representations of groups. |0 http://id.loc.gov/authorities/subjects/sh85112944 | |
| 650 | 0 | |a Convex functions. |0 http://id.loc.gov/authorities/subjects/sh85031728 | |
| 650 | 6 | |a Groupes de Lie. | |
| 650 | 6 | |a Représentations de groupes. | |
| 650 | 6 | |a Fonctions convexes. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Convex functions |2 fast | |
| 650 | 7 | |a Lie groups |2 fast | |
| 650 | 7 | |a Representations of groups |2 fast | |
| 650 | 1 | 7 | |a Lie-algebra's. |2 gtt |
| 650 | 1 | 7 | |a Holomorfe functies. |2 gtt |
| 776 | 0 | 8 | |i Print version: |a Neeb, Karl-Hermann. |t Holomorphy and convexity in Lie theory |z 3110156695 |w (DLC) 99047514 |w (OCoLC)42392206 |
| 830 | 0 | |a De Gruyter expositions in mathematics ; |v 28. |x 0938-6572 |0 http://id.loc.gov/authorities/names/n90653843 | |
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Datensatz im Suchindex
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| contents | Abstract Representation Theory -- Reproducing Kernel Spaces Operator-Valued Positive Definite Kernels The Cone of Positive Definite Kernels Representations of Involutive Semigroups Involutive Semigroups Bounded Representations Hermitian Representations Representations on Reproducing Kernel Spaces Positive Definite Functions on Involutive Semigroups Positive Definite Functions -- the Discrete Case Enveloping C*-algebras Multiplicity Free Representations Continuous and Holomorphic Representations Continuous Representations and Positive Definite Functions Holomorphic Representations of Involutive Semigroups Convex Geometry and Representations of Vector Spaces -- Convex Sets and Convex Functions Convex Sets and Cones Finite Reflection Groups and Convex Sets Convex Functions and Fenchel Duality Laplace Transforms The Characteristic Function of a Convex Set Representations of Cones and Tubes Commutative Representation Theory Representations of Cones Holomorphic Representations of Tubes Realization of Cyclic Representations by Holomorphic Functions Holomorphic Extensions of Unitary Representations Convex Geometry of Lie Algebras -- Convexity in Lie Algebras Compactly Embedded Cartan Subalgebras Root Decompositions Lie Algebras With Many Invariant Convex Sets Convexity Theorems and Their Applications Admissible Coadjoint Orbits and Convexity Theorems The Structure of Admissible Lie Algebras Invariant Elliptic Cones in Lie Algebras Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups -- Unitary Highest Weight Representations: Algebraic Theory Generalized Highest Weight Representations Positive Complex Polarizations Highest Weight Modules of Finite-Dimensional Lie Algebras The Metaplectic Factorization Unitary Highest Weight Representations of Hermitian Lie Algebras Unitary Highest Weight Representations: Analytic Theory The Convex Moment Set of a Unitary Representation Irreducible Unitary Representations The Metaplectic Representation and Its Applications Special Properties of Unitary Highest Weight Representations Moment Sets for C*-algebras Moment Sets for Group Representations Complex Ol'shanskii Semigroups and Their Representations Lawson's Theorem on Ol'shanskii Semigroups Holomorphic Extension of Unitary Representations Holomorphic Representations of Ol'shanskii Semigroups Irreducible Holomorphic Representations Gelfand-Raikov Theorems for Ol'shanskii Semigroups Decomposition and Characters of Holomorphic Representations Realization of Highest Weight Representations on Complex Domains The Structure of Groups of Harish-Chandra Type Representations of Groups of Harish-Chandra Type The Compression Semigroup and Its Representations Hilbert Spaces of Square Integrable Holomorphic Functions Complex Geometry and Representation Theory -- Complex and Convex Geometry of Complex Semigroups Locally Convex Functions and Local Recession Cones Invariant Convex Sets and Functions in Lie Algebras Calculations in Low-Dimensional Cases Biinvariant Plurisubharmonic Functions Complex Semigroups and Stein Manifolds Biinvariant Domains of Holomorphy Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups Biinvariant Hilbert Spaces Hardy Spaces Defined by Sup-Norms Hardy Spaces Defined by Square Integrability The Fine Structure of Hardy Spaces Coherent State Representations Complex Structures on Homogeneous Spaces Heisenberg's Uncertainty Principle and Coherent States Bounded Operators on Hilbert Spaces Spectral Measures and Unbounded Operators Holomorphic Functions on Infinite-Dimensional Spaces Symplectic Geometry Simple Modules of p-Length 2 Symplectic Modules of Convex Type Square Integrable Representations of Locally Compact Groups The Stone-von Neumann-Mackey Theorem |
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| discipline | Mathematik |
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--</subfield><subfield code="g">VIII. 1.</subfield><subfield code="t">Admissible Coadjoint Orbits and Convexity Theorems</subfield><subfield code="g">266 --</subfield><subfield code="g">VIII. 2.</subfield><subfield code="t">The Structure of Admissible Lie Algebras</subfield><subfield code="g">292 --</subfield><subfield code="g">VIII. 3.</subfield><subfield code="t">Invariant Elliptic Cones in Lie Algebras</subfield><subfield code="g">306 --</subfield><subfield code="g">D.</subfield><subfield code="t">Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups --</subfield><subfield code="g">Chapter IX.</subfield><subfield code="t">Unitary Highest Weight Representations: Algebraic Theory</subfield><subfield code="g">327 --</subfield><subfield code="g">IX. 1.</subfield><subfield code="t">Generalized Highest Weight Representations</subfield><subfield code="g">328 --</subfield><subfield code="g">IX. 2.</subfield><subfield code="t">Positive Complex Polarizations</subfield><subfield code="g">344 --</subfield><subfield code="g">IX. 3.</subfield><subfield code="t">Highest Weight Modules of Finite-Dimensional Lie Algebras</subfield><subfield code="g">356 --</subfield><subfield code="g">IX. 4.</subfield><subfield code="t">The Metaplectic Factorization</subfield><subfield code="g">361 --</subfield><subfield code="g">IX. 5.</subfield><subfield code="t">Unitary Highest Weight Representations of Hermitian Lie Algebras</subfield><subfield code="g">374 --</subfield><subfield code="g">Chapter X.</subfield><subfield code="t">Unitary Highest Weight Representations: Analytic Theory</subfield><subfield code="g">387 --</subfield><subfield code="g">X.1.</subfield><subfield code="t">The Convex Moment Set of a Unitary Representation</subfield><subfield code="g">388 --</subfield><subfield code="g">X.2.</subfield><subfield code="t">Irreducible Unitary Representations</subfield><subfield code="g">394 --</subfield><subfield code="g">X.3.</subfield><subfield code="t">The Metaplectic Representation and Its Applications</subfield><subfield code="g">400 --</subfield><subfield code="g">X.4.</subfield><subfield code="t">Special Properties of Unitary Highest Weight Representations</subfield><subfield code="g">411 --</subfield><subfield code="g">X.5.</subfield><subfield code="t">Moment Sets for C*-algebras</subfield><subfield code="g">419 --</subfield><subfield code="g">X.6.</subfield><subfield code="t">Moment Sets for Group Representations</subfield><subfield code="g">428 --</subfield><subfield code="g">Chapter XI.</subfield><subfield code="t">Complex Ol'shanskii Semigroups and Their Representations</subfield><subfield code="g">442 --</subfield><subfield code="g">XI. 1.</subfield><subfield code="t">Lawson's Theorem on Ol'shanskii Semigroups</subfield><subfield code="g">443 --</subfield><subfield code="g">XI. 2.</subfield><subfield code="t">Holomorphic Extension of Unitary Representations</subfield><subfield code="g">457 --</subfield><subfield code="g">XI. 3.</subfield><subfield code="t">Holomorphic Representations of Ol'shanskii Semigroups</subfield><subfield code="g">464 --</subfield><subfield code="g">XI. 4.</subfield><subfield code="t">Irreducible Holomorphic Representations</subfield><subfield code="g">470 --</subfield><subfield code="g">XI. 5.</subfield><subfield code="t">Gelfand-Raikov Theorems for Ol'shanskii Semigroups</subfield><subfield code="g">476 --</subfield><subfield code="g">XI. 6.</subfield><subfield code="t">Decomposition and Characters of Holomorphic Representations</subfield><subfield code="g">477 --</subfield><subfield code="g">Chapter XII.</subfield><subfield code="t">Realization of Highest Weight Representations on Complex Domains</subfield><subfield code="g">493 --</subfield><subfield code="g">XII. 1.</subfield><subfield code="t">The Structure of Groups of Harish-Chandra Type</subfield><subfield code="g">494 --</subfield><subfield code="g">XII. 2.</subfield><subfield code="t">Representations of Groups of Harish-Chandra Type</subfield><subfield code="g">514 --</subfield><subfield code="g">XII. 3.</subfield><subfield code="t">The Compression Semigroup and Its Representations</subfield><subfield code="g">524 --</subfield><subfield code="g">XII. 5.</subfield><subfield code="t">Hilbert Spaces of Square Integrable Holomorphic Functions</subfield><subfield code="g">538 --</subfield><subfield code="g">E.</subfield><subfield code="t">Complex Geometry and Representation Theory --</subfield><subfield code="g">Chapter XIII.</subfield><subfield code="t">Complex and Convex Geometry of Complex Semigroups</subfield><subfield code="g">557 --</subfield><subfield code="g">XIII. 1.</subfield><subfield code="t">Locally Convex Functions and Local Recession Cones</subfield><subfield code="g">559 --</subfield><subfield code="g">XIII. 2.</subfield><subfield code="t">Invariant Convex Sets and Functions in Lie Algebras</subfield><subfield code="g">563 --</subfield><subfield code="g">XIII. 3.</subfield><subfield code="t">Calculations in Low-Dimensional Cases</subfield><subfield code="g">571 --</subfield><subfield code="g">XIII. 4.</subfield><subfield code="t">Biinvariant Plurisubharmonic Functions</subfield><subfield code="g">576 --</subfield><subfield code="g">XIII. 5.</subfield><subfield code="t">Complex Semigroups and Stein Manifolds</subfield><subfield code="g">586 --</subfield><subfield code="g">XIII. 6.</subfield><subfield code="t">Biinvariant Domains of Holomorphy</subfield><subfield code="g">595 --</subfield><subfield code="g">Chapter XIV.</subfield><subfield code="t">Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups</subfield><subfield code="g">600 --</subfield><subfield code="g">XIV. 1.</subfield><subfield code="t">Biinvariant Hilbert Spaces</subfield><subfield code="g">601 --</subfield><subfield code="g">XIV. 2.</subfield><subfield code="t">Hardy Spaces Defined by Sup-Norms</subfield><subfield code="g">608 --</subfield><subfield code="g">XIV. 3.</subfield><subfield code="t">Hardy Spaces Defined by Square Integrability</subfield><subfield code="g">616 --</subfield><subfield code="g">XIV. 4.</subfield><subfield code="t">The Fine Structure of Hardy Spaces</subfield><subfield code="g">623 --</subfield><subfield code="g">Chapter XV.</subfield><subfield code="t">Coherent State Representations</subfield><subfield code="g">645 --</subfield><subfield code="g">XV. 1.</subfield><subfield code="t">Complex Structures on Homogeneous Spaces</subfield><subfield code="g">646 --</subfield><subfield code="g">XV. 2.</subfield><subfield code="t">Coherent State Representations</subfield><subfield code="g">650 --</subfield><subfield code="g">XV. 3.</subfield><subfield code="t">Heisenberg's Uncertainty Principle and Coherent States</subfield><subfield code="g">656 --</subfield><subfield code="g">Appendix I.</subfield><subfield code="t">Bounded Operators on Hilbert Spaces</subfield><subfield code="g">665 --</subfield><subfield code="g">Appendix II.</subfield><subfield code="t">Spectral Measures and Unbounded Operators</subfield><subfield code="g">677 --</subfield><subfield code="g">Appendix III.</subfield><subfield code="t">Holomorphic Functions on Infinite-Dimensional Spaces</subfield><subfield code="g">686 --</subfield><subfield code="g">Appendix IV.</subfield><subfield code="t">Symplectic Geometry</subfield><subfield code="g">694 --</subfield><subfield code="g">Appendix V.</subfield><subfield code="t">Simple Modules of p-Length 2</subfield><subfield code="g">705 --</subfield><subfield code="g">Appendix VI.</subfield><subfield code="t">Symplectic Modules of Convex Type</subfield><subfield code="g">715 --</subfield><subfield code="g">Appendix VII.</subfield><subfield code="t">Square Integrable Representations of Locally Compact Groups</subfield><subfield code="g">727 --</subfield><subfield code="g">Appendix VIII.</subfield><subfield code="t">The Stone-von Neumann-Mackey 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| id | ZDB-4-EBA-ocn857492977 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:31Z |
| institution | BVB |
| isbn | 9783110808148 3110808145 |
| issn | 0938-6572 ; |
| language | English |
| oclc_num | 857492977 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 778 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Walter de Gruyter, |
| record_format | marc |
| series | De Gruyter expositions in mathematics ; |
| series2 | De Gruyter expositions in mathematics, |
| spelling | Neeb, Karl-Hermann. Holomorphy and convexity in Lie theory / by Karl-Hermann Neeb. New York : Walter de Gruyter, 2000. 1 online resource (xxi, 778 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter expositions in mathematics, 0938-6572 ; 28 Includes bibliographical references (pages 751-766) and index. A. Abstract Representation Theory -- Chapter I. Reproducing Kernel Spaces 3 -- I.1. Operator-Valued Positive Definite Kernels 3 -- I.2. The Cone of Positive Definite Kernels 14 -- Chapter II. Representations of Involutive Semigroups 20 -- II. 1. Involutive Semigroups 21 -- II. 2. Bounded Representations 24 -- II. 3. Hermitian Representations 29 -- II. 4. Representations on Reproducing Kernel Spaces 34 -- Chapter III. Positive Definite Functions on Involutive Semigroups 52 -- III. 1. Positive Definite Functions -- the Discrete Case 53 -- III. 2. Enveloping C*-algebras 68 -- III. 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.1. 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 -- 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. 1. 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.1. 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 -- Chapter XI. Complex Ol'shanskii 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-Raikov 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. 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. 1. 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 -- 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. Print version record. Lie groups. http://id.loc.gov/authorities/subjects/sh85076786 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Convex functions. http://id.loc.gov/authorities/subjects/sh85031728 Groupes de Lie. Représentations de groupes. Fonctions convexes. MATHEMATICS Algebra Intermediate. bisacsh Convex functions fast Lie groups fast Representations of groups fast Lie-algebra's. gtt Holomorfe functies. gtt Print version: Neeb, Karl-Hermann. Holomorphy and convexity in Lie theory 3110156695 (DLC) 99047514 (OCoLC)42392206 De Gruyter expositions in mathematics ; 28. 0938-6572 http://id.loc.gov/authorities/names/n90653843 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=627685 Volltext |
| spellingShingle | Neeb, Karl-Hermann Holomorphy and convexity in Lie theory / De Gruyter expositions in mathematics ; Abstract Representation Theory -- Reproducing Kernel Spaces Operator-Valued Positive Definite Kernels The Cone of Positive Definite Kernels Representations of Involutive Semigroups Involutive Semigroups Bounded Representations Hermitian Representations Representations on Reproducing Kernel Spaces Positive Definite Functions on Involutive Semigroups Positive Definite Functions -- the Discrete Case Enveloping C*-algebras Multiplicity Free Representations Continuous and Holomorphic Representations Continuous Representations and Positive Definite Functions Holomorphic Representations of Involutive Semigroups Convex Geometry and Representations of Vector Spaces -- Convex Sets and Convex Functions Convex Sets and Cones Finite Reflection Groups and Convex Sets Convex Functions and Fenchel Duality Laplace Transforms The Characteristic Function of a Convex Set Representations of Cones and Tubes Commutative Representation Theory Representations of Cones Holomorphic Representations of Tubes Realization of Cyclic Representations by Holomorphic Functions Holomorphic Extensions of Unitary Representations Convex Geometry of Lie Algebras -- Convexity in Lie Algebras Compactly Embedded Cartan Subalgebras Root Decompositions Lie Algebras With Many Invariant Convex Sets Convexity Theorems and Their Applications Admissible Coadjoint Orbits and Convexity Theorems The Structure of Admissible Lie Algebras Invariant Elliptic Cones in Lie Algebras Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups -- Unitary Highest Weight Representations: Algebraic Theory Generalized Highest Weight Representations Positive Complex Polarizations Highest Weight Modules of Finite-Dimensional Lie Algebras The Metaplectic Factorization Unitary Highest Weight Representations of Hermitian Lie Algebras Unitary Highest Weight Representations: Analytic Theory The Convex Moment Set of a Unitary Representation Irreducible Unitary Representations The Metaplectic Representation and Its Applications Special Properties of Unitary Highest Weight Representations Moment Sets for C*-algebras Moment Sets for Group Representations Complex Ol'shanskii Semigroups and Their Representations Lawson's Theorem on Ol'shanskii Semigroups Holomorphic Extension of Unitary Representations Holomorphic Representations of Ol'shanskii Semigroups Irreducible Holomorphic Representations Gelfand-Raikov Theorems for Ol'shanskii Semigroups Decomposition and Characters of Holomorphic Representations Realization of Highest Weight Representations on Complex Domains The Structure of Groups of Harish-Chandra Type Representations of Groups of Harish-Chandra Type The Compression Semigroup and Its Representations Hilbert Spaces of Square Integrable Holomorphic Functions Complex Geometry and Representation Theory -- Complex and Convex Geometry of Complex Semigroups Locally Convex Functions and Local Recession Cones Invariant Convex Sets and Functions in Lie Algebras Calculations in Low-Dimensional Cases Biinvariant Plurisubharmonic Functions Complex Semigroups and Stein Manifolds Biinvariant Domains of Holomorphy Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups Biinvariant Hilbert Spaces Hardy Spaces Defined by Sup-Norms Hardy Spaces Defined by Square Integrability The Fine Structure of Hardy Spaces Coherent State Representations Complex Structures on Homogeneous Spaces Heisenberg's Uncertainty Principle and Coherent States Bounded Operators on Hilbert Spaces Spectral Measures and Unbounded Operators Holomorphic Functions on Infinite-Dimensional Spaces Symplectic Geometry Simple Modules of p-Length 2 Symplectic Modules of Convex Type Square Integrable Representations of Locally Compact Groups The Stone-von Neumann-Mackey Theorem Lie groups. http://id.loc.gov/authorities/subjects/sh85076786 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Convex functions. http://id.loc.gov/authorities/subjects/sh85031728 Groupes de Lie. Représentations de groupes. Fonctions convexes. MATHEMATICS Algebra Intermediate. bisacsh Convex functions fast Lie groups fast Representations of groups fast Lie-algebra's. gtt Holomorfe functies. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85076786 http://id.loc.gov/authorities/subjects/sh85112944 http://id.loc.gov/authorities/subjects/sh85031728 |
| title | Holomorphy and convexity in Lie theory / |
| title_alt | Abstract Representation Theory -- Reproducing Kernel Spaces Operator-Valued Positive Definite Kernels The Cone of Positive Definite Kernels Representations of Involutive Semigroups Involutive Semigroups Bounded Representations Hermitian Representations Representations on Reproducing Kernel Spaces Positive Definite Functions on Involutive Semigroups Positive Definite Functions -- the Discrete Case Enveloping C*-algebras Multiplicity Free Representations Continuous and Holomorphic Representations Continuous Representations and Positive Definite Functions Holomorphic Representations of Involutive Semigroups Convex Geometry and Representations of Vector Spaces -- Convex Sets and Convex Functions Convex Sets and Cones Finite Reflection Groups and Convex Sets Convex Functions and Fenchel Duality Laplace Transforms The Characteristic Function of a Convex Set Representations of Cones and Tubes Commutative Representation Theory Representations of Cones Holomorphic Representations of Tubes Realization of Cyclic Representations by Holomorphic Functions Holomorphic Extensions of Unitary Representations Convex Geometry of Lie Algebras -- Convexity in Lie Algebras Compactly Embedded Cartan Subalgebras Root Decompositions Lie Algebras With Many Invariant Convex Sets Convexity Theorems and Their Applications Admissible Coadjoint Orbits and Convexity Theorems The Structure of Admissible Lie Algebras Invariant Elliptic Cones in Lie Algebras Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups -- Unitary Highest Weight Representations: Algebraic Theory Generalized Highest Weight Representations Positive Complex Polarizations Highest Weight Modules of Finite-Dimensional Lie Algebras The Metaplectic Factorization Unitary Highest Weight Representations of Hermitian Lie Algebras Unitary Highest Weight Representations: Analytic Theory The Convex Moment Set of a Unitary Representation Irreducible Unitary Representations The Metaplectic Representation and Its Applications Special Properties of Unitary Highest Weight Representations Moment Sets for C*-algebras Moment Sets for Group Representations Complex Ol'shanskii Semigroups and Their Representations Lawson's Theorem on Ol'shanskii Semigroups Holomorphic Extension of Unitary Representations Holomorphic Representations of Ol'shanskii Semigroups Irreducible Holomorphic Representations Gelfand-Raikov Theorems for Ol'shanskii Semigroups Decomposition and Characters of Holomorphic Representations Realization of Highest Weight Representations on Complex Domains The Structure of Groups of Harish-Chandra Type Representations of Groups of Harish-Chandra Type The Compression Semigroup and Its Representations Hilbert Spaces of Square Integrable Holomorphic Functions Complex Geometry and Representation Theory -- Complex and Convex Geometry of Complex Semigroups Locally Convex Functions and Local Recession Cones Invariant Convex Sets and Functions in Lie Algebras Calculations in Low-Dimensional Cases Biinvariant Plurisubharmonic Functions Complex Semigroups and Stein Manifolds Biinvariant Domains of Holomorphy Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups Biinvariant Hilbert Spaces Hardy Spaces Defined by Sup-Norms Hardy Spaces Defined by Square Integrability The Fine Structure of Hardy Spaces Coherent State Representations Complex Structures on Homogeneous Spaces Heisenberg's Uncertainty Principle and Coherent States Bounded Operators on Hilbert Spaces Spectral Measures and Unbounded Operators Holomorphic Functions on Infinite-Dimensional Spaces Symplectic Geometry Simple Modules of p-Length 2 Symplectic Modules of Convex Type Square Integrable Representations of Locally Compact Groups The Stone-von Neumann-Mackey Theorem |
| 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 | Lie groups. http://id.loc.gov/authorities/subjects/sh85076786 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Convex functions. http://id.loc.gov/authorities/subjects/sh85031728 Groupes de Lie. Représentations de groupes. Fonctions convexes. MATHEMATICS Algebra Intermediate. bisacsh Convex functions fast Lie groups fast Representations of groups fast Lie-algebra's. gtt Holomorfe functies. gtt |
| topic_facet | Lie groups. Representations of groups. Convex functions. Groupes de Lie. Représentations de groupes. Fonctions convexes. MATHEMATICS Algebra Intermediate. Convex functions Lie groups Representations of groups Lie-algebra's. Holomorfe functies. |
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| work_keys_str_mv | AT neebkarlhermann holomorphyandconvexityinlietheory |