Zeros of operators on real entire functions of order less than two (Q1076193)

This note is motivated, in part, by the following conjecture of \textit{G. Pólya} [Q. J. Math., Oxf. Ser. 1, 21-34 (1930)] and \textit{A. Wiman} [Math. Ann. 104, 169-181 (1930; Zbl 0001.02202)]: If a real entire function f(x) of order less than two has only a finite number of nonreal zeros, then there is a positive integer M such that if \(m\geq M\), then \(f^{(m)}(x)\) has only real zeros. Recently, T. Craven, W. Smith and the reviewer have proved the Pólya-Wiman conjecture. In the paper under review, the author establishes results related to these ideas when differentiation is, however, replaced by more general differential operators.