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Causal Symmetric Spaces - 1st Edition - ISBN: 9780125254304, 9780080528724

Causal Symmetric Spaces, Volume 18

1st Edition

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Series Editor: Sigurdur Helgason
Authors: Gestur Olafsson Joachim Hilgert
eBook ISBN: 9780080528724
Imprint: Academic Press
Published Date: 15th August 1996
Page Count: 286
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Table of Contents

Symmetric Spaces: Basic Structure Theory. Dual Symmetric Spaces. The Module Structure of q. A-subspaces. The Hyperboloids. Causal Orientations: Covex Cones and their Automorphisms. Causal Orientations. Semigroups. The Order Compactification. Examples. Symmetric Spaces Related to Tube Domains. Irreducible Causal Symmetric Spaces: Existence of Causal Structures. The Classification of Causal Symmetric Pairs. Clasification of Invariant Cones: SymmetricSL(2, R)-Reduction. The Minimal and Maximal Cones. The Linear Convexity Theorem. The Classification. Extension of Cones. The Geometry: The Bounded Realization of H / H ( K. The Semigroup S(C). The Causal Intervals. Compression Semigroups. The Non-Linear Convexity Theorem. The B<+>#-Order. The Affine Closure of B<+>#. The Order Compactification: Causal Galois Connections. An Alternative Realization of M<+>cpt. NOTE: THE cpt SHOULD APPEAR DIRECTLY OVER A + SIGN. The Stabilizers for M<+>cpt. SEE NOTE. Theo Orbit Structure of M<+>cpt. (NO + SIGN.) The Space SL(3, R)/SO(2,1). Holomorphic Representations: Holomorphic Representations of Semigroups. Highest Weight-Modules. The Holomorphic Discrete Series. Classical Hardy Spaces. Hardy Spaces. The Cauchy-Szegi Kernel. Spherical Functions: The Classical Laplace Transform. Spherical Functions. The Asymptotics. Expansion Formula. The Spherical Laplace Transform. The Abel Transform. Relation to Representation Theory. The Wiener-Hopf Algebra. Appendices. Notation. References. Bibliography. Author Index. Subject Index.


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.

Key Features

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 spaces

Deals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fields

Presents basic geometric properties of semi-simple symmetric spaces

Includes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces


Advanced students and researchers in geometry and analysis on causal symmetric spaces


No. of pages:
© Academic Press 1996
15th August 1996
Academic Press
eBook ISBN:


@qu:"This book is an excellent introduction to the geometry and structure of casual symmetric spaces. It should be accessible to any graduate student with a solid Lie-theoretic background." @source:--Karl-Hermann Neeb, MATHEMATICAL REVIEWS

Ratings and Reviews

About the Series Editor

Sigurdur Helgason

Affiliations and Expertise

Massachusetts Institute of Technology

About the Authors

Gestur Olafsson

Gestur Olafsson studied at the University of Iceland and University of Gottingen. He completed his doctorial thesis in 1982,and worked at the University of Gottingen until 1991. He is currently an Associate Professor at the University of Roskilde, and has had Tenure at Louisiana State University since 1994.

Affiliations and Expertise

Louisiana State University

Joachim Hilgert

Joachim Hilgert studied at Universitat at Munchen and at Tule University. He received the DFG-Heisenberg grant 1991-1993. Hilgert has been a Professor at the TU Clausthal since 1993.

Affiliations and Expertise

University of Wisconsin