Linear finite difference operators preserving Laguerre-Pólya class

Abstract

We completely describe all finite difference operators of the form $${\Delta }_{M_1,M_2,h}(f)(z)=M_1(z)f(z+h)+M_2(z)f(z-h)$$ preserving the Laguerre-Pólya class of entire functions. Here $M_1$ and $M_2$ are some complex functions and $h$ is a nonzero complex number.

10 pages

References in corpus (2)

• Polynomials, roots, and interlacing
• Complex zero strip decreasing operators

Cited by in corpus (1)

• Hermite-Poulain theorems for linear finite difference operators