Holomorphy and Convexity in Lie Theory / / Karl-Hermann Neeb.

• Superior document: Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package
• VerfasserIn: Neeb, Karl-Hermann,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2000
• Year of Publication: 2011
• Edition: Reprint 2011
• Language: English
• Series: De Gruyter Expositions in Mathematics , 28
• Physical Description: 1 online resource (778 p.) :; Num. figs.

Table of 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’shanskiĭ 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