Linear q-difference, difference and differential operators preserving some \mathcal{A}-entire functions.

We apply Rossi's half-plane version of Borel's theorem to study the zero distribution of linear combinations of \mathcal {A}-entire functions (Theorem 1.2). This provides a unified way to study linear q-difference, difference and differential operators (with entire coefficients) preserving subsets of \mathcal {A}-entire functions, and hence obtain several analogous results for the Hermite-Poulain theorem to linear finite (q-)difference operators with polynomial coefficients. The method also produces a result on the existence of infinitely many non-real zeros of some differential polynomials of functions in certain sub-classes of \mathcal {A}-entire functions. [ABSTRACT FROM AUTHOR]