A sampling theorem on homogeneous manifolds

Abstract

We consider a generalization of entire functions of spherical exponential type and Lagrangian splines on manifolds. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a manifold is uniquely determined by its values on some discrete sets of points.The main result of the paper is a formula for reconstruction of spectral entire functions from their values on discrete sets using Lagrangian splines.