A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane

A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane H realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on H. An iterative algorithm is presented, which allows to reconstruct bandlimited 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.