The Recovery of Irregularly Sampled Band Limited Functions via Tempered Splines

We show that band limited functions can be recovered from their values on certain irregularly distributed discrete sampling sets as the limits of the piecewise polynomial spline interpolants when the order of the splines goes to infinity. This is an extension of the classical case when the sampling set is a lattice which was considered by Collatz, Quade, Schoenberg, and others.