Linear q-difference, difference and differential operators preserving some A-entire functions

2022/11/15 by Jiaxing Huang, Huang, Jiaxing, Tuen Wai Ng +1
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2211.07856

openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply Rossi's half-plane version of Borel's Theorem to study the zero distribution of linear combinations of 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 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 A-entire functions.

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