Analysis and Geometry on Complex Homogeneous Domains

Part 1 Function spaces on complex semi-groups, Jacques Faraut: Hilbert spaces of holomorphic functions; invariant cones and complex semi-groups; positive unitary representations; Hilbert function spaces on complex semi-groups; Hilbert function spaces on SL(2,C); Hilbert function spaces on a complex semi-simple Lie group. Part 2 Graded Lie algebras and pseudo-hermitian symmetric spaces, Soji Kaneyuki: semi-simple graded Lie algebras; symmetric R-spaces; pseudo-hermitian symmetric spaces. Part 3 Function spaces on bounded symmetric domains, Adam Koranyi: Bergman kernel and Bergman metric; symmetric domains and symmetric spaces; construction of the hermitian symmetric spaces; structure of symmetric domains; the weighted Bergman spaces; differential operators; function spaces. Part 4 The heat kernels of non-compact symmetric spaces, Qi-keng Lu: introduction; the Laplace-Beltrami operator in various co-ordinates; the integral transformations; the heat kernel of the hyperball Rr(m,n); the harmonic forms on the complex Grassmann manifold; the horo-hypercircle coordinate of a complex hyperball; the heat kernel of R11(m); the matrix representation of NIRGSS. Part 5 Jordan triple systems, Guy Ross: polynomial identities; Jordan algebras; the quasi-inverse; the generic minimal polynomial; tripotents and Pierce decomposition; hermitian positive JTS; further results and open problems. References.