Title

On the Convergence of One Parameter Families of Interpolators

Date of Completion

January 2011

Keywords

Mathematics

Degree

Ph.D.

Abstract

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. ^