Recovery of bivariate band-limited functions using scattered translates of the Poisson kernel

Abstract

This paper continues the study of interpolation operators on scattered data. We introduce the Poisson interpolation operator and prove various properties of this operator. The main result concerns functions whose Fourier transforms are concentrated near the origin, specifically functions belonging to the Paley–Wiener space PWBβ. We show that one may recover these functions from their samples on a complete interpolating sequence for [−δ,δ]2 by using the Poisson interpolation operator, provided that 0<β<(3−8)δ.