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

In both Lyubarskii and Madych (1994) [7], and Schlumprecht and Sivakumar (2009) [9], it was 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 ϕ(x)ϕ(x), called an interpolator, so that scattered translates of this function may be used to interpolate and recover any given Paley–Wiener function.