Non-oscillating Paley-Wiener functions (Q2765887)

A real Paley-Wiener function (PW-function) is an entire function, \(f\), of exponential type such that \(f\in L_2(\mathbb R)\) and \(f(\mathbb R)\subset \mathbb R\). J. R. Higgins posed the question whether or not some derivative of an arbitrary real Paley-Wiener function has infinitely many real zeros. In this interesting paper, the authors construct a wide class of real PW-functions, \(f\), with the property that each derivative, \(f^{(n)}\), \(n=0,1,2\dots\), has only a finite number of real zeros. Moreover, they obtain a result (Theorem 2) which gives a sharp asymptotic estimate (as \(n\to\infty\)) of the length of the smallest interval which contains all the real zeros of \(f^{(n)}\).