  A notion of band limited functions is considered in the case of the
hyperbolic plane in its Poincare upper half-plane $\mathbb{H}$ realization. The
concept of band-limitedness is based on the existence of the Helgason-Fourier
transform on $\mathbb{H}$. An iterative algorithm is presented, which allows to
reconstruct band-limited functions from some countable sets of their values. It
is shown that for sufficiently dense metric lattices a geometric rate of
convergence can be guaranteed as long as the sampling density is high enough
compared to the band-width of the sampled function.
