On Shifts of the Sequence of Integers Generating Functions that are Invertible in the Sense of Ehrenpreis

Abstract

We consider the Schwartz algebra $$ \mathcal{P} $$ which consists of all entire functions of exponential type having the polynomial growth along the real axis. Given an unbounded function l : [0;+∞) → ℝ, we study under which conditions the perturbed sequence {k + l(|k|)}, k =±1,±2,…, forms the zero set of the function that is invertible in the sense of Ehrenpreis.