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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 completeinterpolating sequence for $[-\delta,\delta]^2$ by using the Poissoninterpolation operator, provided that $0<\beta < (3-\sqrt{8})\delta$.

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