Linear finite difference operators preserving Laguerre-Pólya class

2016/08/12 by Olga Katkova, Katkova, O., Mikhail Tyaglov +3
Mathematics · #26C10 #30C15 #30D15 #30D35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1608.03924

openalex publication_date 2016/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We completely describe all finite difference operators of the form Δ_{M1, M2, h}(f)(z)=M₁(z) f(z+h) + M₂(z) f(z-h) preserving the Laguerre-Pólya class of entire functions. Here M₁ and M₂ are some complex functions and h is a nonzero complex number.

Citations

• Elements of Polya-Schur theory in finite difference setting

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