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

This paper continues the study of interpolation operators on scattered data. We introduce the Poisson interpolation operator and prove various properties. The main result concerns functions in the Paley-Wiener space $PW_{B_\beta}$, and shows that one may recover these functions from their samples on a complete interpolating sequence for $[-\delta,\delta]^2$ by using the Poisson interpolation operator, provided that $0<\beta < (3-\sqrt{8})\delta$.