Olafsson, G., Hilgert, J. 　著

内容

目次

Symmetric spaces: basic structure theory, dual symmetric spaces, themodule structure of q, a-subspaces, the hyperboloids. Causalorientations: covex cones and their auto-morphisms, causalorientations, semigroups, the order compactification, examples,symmetric spaces related to tube domains. Irreducible causal symmetricspaces: existence of causal structures, the classification of causalsymmetric pairs. Classification of invariant cones: symmetricSL(2,R)-reduction, the minimal and maximal cones, the linear con-vexitytheorem, the classification, extension of cones. The geometry: thebounded realisation of HHnK, 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 galoisconnections, an alternative realisation of M+, the stabilisers for M+,theo orbit structure of M, the space SL(3,R)/SO(2,1). Holo-morphicrepresentations: holomorphic representations of semi-groups, highestweight-modules, the holomorphic discrete series, classical hardyspaces, hardy spaces, the cauchy-szego kernel. Spherical functions: theclassical laplace transform, spherical functions, the asymptotics,expansion formula, the spherical laplace transform, the abel transform,relation to representation theory. The wiener-hopf algebra.