Linear finite difference operators with constant coefficients and distribution of zeros of polynomials

TL;DR

This paper investigates how finite difference operators of finite order influence the zero distribution of polynomials and entire functions, providing insights into their structural properties.

Contribution

It introduces a detailed analysis of the impact of finite difference operators with constant coefficients on zero distributions, a novel perspective in polynomial and entire function theory.

Findings

Finite difference operators can alter zero distributions in predictable ways.

The study characterizes the zero distribution changes under these operators.

Results have implications for stability analysis in polynomial equations.

Abstract

We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.