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Title Holomorphy and Convexity in Lie Theory.
Imprint Berlin : De Gruyter.


 Internet  Electronic Book    AVAILABLE
Description Online-Ressource.
Series De Gruyter Expositions in Mathematics ; 28
Note Available only to authorized UTEP users.
Subject Convex functions.
Lie groups.
Representations of groups.
Contents Frontmatter -- A. Abstract Representation Theory -- Chapter I. Reproducing Kernel Spaces -- Chapter II. Representations of Involutive Semigroups -- Chapter III. Positive Definite Functions on Involutive Semigroups -- Chapter IV. Continuous and Holomorphic Representations -- B. Convex Geometry and Representations of Vector Spaces -- Chapter V. Convex Sets and Convex Functions -- Chapter VI. Representations of Cones and Tubes -- C. Convex Geometry of Lie Algebras -- Chapter VII. Convexity in Lie Algebras -- Chapter VIII. Convexity Theorems and Their Applications -- D. Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups -- Chapter IX. Unitary Highest Weight Representations: Algebraic Theory -- Chapter X. Unitary Highest Weight Representations: Analytic Theory -- Chapter XI. Complex Ol'shanskiń≠ Semigroups and Their Representations -- Chapter XII. Realization of Highest Weight Representations on Complex Domains -- E. Complex Geometry and Representation Theory -- Chapter XIII. Complex and Convex Geometry of Complex Semigroups -- Chapter XIV. Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups -- Chapter XV. Coherent State Representations -- Appendices -- Appendix I. Bounded Operators on Hilbert Spaces -- Appendix II. Spectral Measures and Unbounded Operators -- Appendix III. Holomorphic Functions on Infinite-Dimensional Spaces -- Appendix IV. Symplectic Geometry -- Appendix V. Simple Modules of p-Length 2 -- Appendix VI. Symplectic Modules of Convex Type -- Appendix VII. Square Integrable Representations of Locally Compact Groups -- Appendix VIII. The Stone -- von Neumann-Mackey Theorem -- Bibliography -- List of Symbols -- Index.
Other Author GBV, 703. Thesis advisor.