On the Convergence of One Parameter Families of Interpolators

The goal of this work is to extend the results of [4] and [7]. Both of these works focus on specific examples which allow on to reconstruct a function from the Paley Wiener class given its samples on a complete interpolating sequence. A theorem is proved which allows us to generalize the work in these two papers. New examples are given after the proof of the theorem. Additionally, a similar theorem is proved for the case of sampling on the integer lattice. This result should be seen as an extension to [5]. After the proof of the theorem, several novel examples are worked out.