  Let $M$ be a Riemmanian manifold with bounded geometry. We consider a
generalization of Paley-Wiener functions and Lagrangian splines on $M$. An
analog of the Paley-Wiener theorem is given. We also show that every
Paley-Wiener function on a manifold is uniquely determined by its values on
some discrete sets of points.
  The main result of the paper is a generalization of the Whittaker-Shannon
formula for reconstruction of a Paley-Wiener function from its values on a
discrete set. It is shown that every Paley- Wiener function on $M$ is a limit
of some linear combinations of fundamental solutions of the powers of the
Laplace-Beltrami operator.
  The result is new even in the one-dimentional case.
