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