Recovery of Paley-Wiener functions using scattered translates of regular interpolators

TL;DR

This paper establishes conditions under which scattered translates of certain interpolator functions can be used to recover Paley-Wiener functions from their values, extending interpolation techniques.

Contribution

It provides a sufficient condition on the interpolator function for effective scattered translation-based recovery of Paley-Wiener functions.

Findings

Identifies a sufficient condition on the interpolator function

Demonstrates the recovery of Paley-Wiener functions from scattered data

Extends interpolation theory for Paley-Wiener functions

Abstract

It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\phi(x)$, called an interpolator, so that scattered translates of this function may be used to interpolate and recover any given Paley-Wiener function.