A Reconstruction Theorem for Riemannian Symmetric Spaces of Noncompact Type

Let f be a rapidly decreasing radial function on a Riemannian symmetric space of noncompact type whose spherical Fourier transform has compact support. We prove a reconstruction theorem which recovers f from the values of an integral operator applied to f on a discrete subset. When G/K is of the complex type we prove a sampling formula recovering f from its own values on a discrete subset. We give explicit results for three dimensional hyperbolic space.