Causal Symmetric Spaces

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. 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.

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.