Causal Symmetric Spaces

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 Mcpt. NOTE: THE cpt SHOULD APPEAR DIRECTLY OVER A + SIGN. The Stabilizers for Mcpt. SEE NOTE. Theo Orbit Structure of Mcpt. (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.