  It is shown that Paley-Wiener functions on Riemannian manifolds of bounded
geometry can be reconstructed in a stable way from some countable sets of their
inner products with certain distributions of compact support. A reconstruction
method in terms of frames is given which is a generalization of the classical
result of Duffin-Schaeffer about exponential frames on intervals. All results
are specified in the case of the two-dimensional hyperbolic space in its
Poincare upper half-plane realization.
