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

Format:

Book

Author/Creator:

Neeb, Karl-Hermann, author.

Series:

De Gruyter expositions in mathematics ; 28

De Gruyter Expositions in Mathematics ; 28

Language:

English

Subjects (All):

Convex functions.

Lie groups.

Representations of groups.

Physical Description:

1 online resource (804 p.)

Edition:

Reprint 2011

Place of Publication:

Berlin ; Boston : De Gruyter, [2011]

Language Note:

English

Summary:

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair , Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann , Columbia University, New York, USA Markus J. Pflaum , University of Colorado, Boulder, USA Dierk Schleicher , Jacobs University, Bremen, Germany Katrin Wendland , University of Freiburg, Germany Honorary Editor Victor P. Maslov , Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups , Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (pages [751]-766) and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9783110808148

3110808145

OCLC:

868974256