Representation theory, Radon transform and the heat equation on a Riemannian symmetric space

Let X=G/K be a Riemannian symmetric space of the noncompact type. We give a short exposition of the representation theory related to X, and discuss its holomorphic extension to the complex crown, a G-invariant subdomain in the complexified symmetric space X_\C=G_\C/K_\C. Applications to the heat transform and the Radon transform for X are given

The c-function for non-compactly causal symmetric spaces

In this paper we prove the product formula for the c-function of non-compactly causal symmetric spaces

A local Paley-Wiener theorem for compact symmetric spaces

The Fourier coefficients of a smooth $K$-invariant function on a compact symmetric space $M=U/K$ are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we describe the size of the support by means of the exponential type of a holomorphic extension of the Fourier coefficient

The c-function for non-compactly causal symmetric spaces and its relations to harmonic analysis and representation theory

We give an overview on the c-function of a non-compactly causal symmetric space G/H and explain its interplay with harmonic analysis and representation theory.Comment: 24 pages. Minor errors corrected, new format. To appear in the Karpelevic memorial volume (AMS series Translations 2