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

Abstract

HANS FEICHTINGER AND ISAAC PESENSONAbstract. A notion of band limited functions is considered in the case of thehyperbolic plane in its Poincare upper half-plane Hrealization. The concept ofband-limitedness is based on the existence of the Helgason-Fourier transformon H. An iterative algorithm is presented, which allows to reconstruct band-limited functions from some countable sets of their values. It is shown thatfor sufficiently dense metric lattices a geometric rate of convergence can beguaranteed as long as the sampling density is high enough compared to theband-width of the sampled function.