Causal symmetric spaces : geometry and harmonic analysis / Joachim Hilgert, Gestur Olafsson.

Format:

Book

Author/Creator:

Hilgert, Joachim.

Contributor:

Ólafsson, Gestur.

Series:

Perspectives in mathematics ; v. 18.

Perspectives in mathematics ; v. 18

Language:

English

Subjects (All):

Symmetric spaces.

Harmonic analysis.

Physical Description:

1 online resource (303 p.)

Place of Publication:

San Diego : Academic Press, c1997.

Language Note:

English

Summary:

This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symm

Contents:

Front Cover; Causal Symmetric Spaces: Geometry and Harmonic Analysis; Copyright Page; Contents; Preface; Introduction; Chapter 1. Symmetric Spaces; 1.1 Basic Structure Theory; 1.2 Dual Symmetric Spaces; 1.3 The Module Structure of To(G/H); 1.4 A-Subspaces; 1.5 The Hyperboloids; Chapter 2. Causal Orientations; 2.1 Convex Cones and Their Automorphisms; 2.2 Causal Orientations; 2.3 Semigroups; 2.4 The Order Compactification; 2.5 Examples; 2.6 Symmetric Spaces Related to Tube Domains; Chapter 3. Irreducible Causal Symmetric Spaces; 3.1 Existence of Causal Structures

3.2 The Classification of Causal Symmetric PairsChapter 4. Classification of Invariant Cones; 4.1 Symmetric SL(2, R) Reduction; 4.2 The Minimal and Maximal Cones; 4.3 The Linear Convexity Theorem; 4.4 The Classification; 4.5 Extension of Cones; Chapter 5. The Geometry; 5.1 The Bounded Realization of H/H H K; 5.2 The Semigroup S(C); 5.3 The Causal Intervals; 5.4 Compression Semigroups; 5.5 The Nonlinear Convexity Theorem; 5.6 The B# - Order; 5.7 The Affine Closure of B#; Chapter 6. The Order Compactification; 6.1 Causal Galois Connections; 6.2 An Alternative Realization of M cpt+

6.3 The Stabilizers for Mcpt+6.4 The Orbit Structure of Mcpt+; 6.5 The Space SL(3,R)/SO(2,1); Chapter 7. Holomorphic Representations; 7.1 Holomorphic Representations of Semigroups; 7.2 Highest-Weight Modules; 7.3 The Holomorphic Discrete Series; 7.4 Classical Hardy Spaces; 7.5 Hardy Spaces; 7.6 The Cauchy-Szegö Kernel; Chapter 8. Spherical Functions; 8.1 The Classical Laplace Transform; 8.2 Spherical Functions; 8.3 The Asymptotics; 8.4 Expansion Formula; 8.5 The Spherical Laplace Transform; 8.6 The Abel Transform; 8.7 Relation to Representation Theory; Chapter 9. The Wiener-Hopf Algebra

Appendix A. Reductive Lie GroupsA.1 Notation; A.2 Finite-Dimensional Representations; A.3 Hermitian Groups; Appendix B. The Vietoris Topology; Notation; Bibliography; Index; Perspectives in Mathematics

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 272-283) and index.

ISBN:

1-281-05487-9

9786611054878

0-08-052872-4

OCLC:

476102643