Causal Symmetric Spaces

Gestur Olafsson, Joachim Hilgert, Sigurdur Helgason

• Publisher: Academic Press
• Year: 1996
• Print ISBN: 9780125254304
• eBook ISBN: 9780080528724
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

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 symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces

Table of contents

• Front Cover
• Causal Symmetric Spaces: Geometry and Harmonic Analysis
• Copyright Page
• Contents
• Preface
• Introduction
• Chapter 1. Symmetric Spaces
• Chapter 2. Causal Orientations
• Chapter 3. Irreducible Causal Symmetric Spaces
• Chapter 4. Classification of Invariant Cones
• Chapter 5. The Geometry
• Chapter 6. The Order Compactification
• Chapter 7. Holomorphic Representations
• Chapter 8. Spherical Functions
• Chapter 9. The Wiener-Hopf Algebra
• Appendix A. Reductive Lie Groups
• Appendix B. The Vietoris Topology
• Notation
• Bibliography
• Index
• Perspectives in Mathematics