A sampling theorem on homogeneous manifolds

We consider a generalization of entire functions of spherical exponential t ype and Lagrangian splines on manifolds. An analog of the Paley-Wiener theo rem is given. We also show that every spectral entire function on a manifol d 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 en tire functions from their values on discrete sets using Lagrangian splines.