Elements of Pólya-Schur theory in the finite difference setting

DOI10.1090/proc/13115zbMath1353.26012arXiv1204.2963OpenAlexW1496142212MaRDI QIDQ2821743

Ilia Krasikov, Petter Brändén, Boris Zalmanovich Shapiro

Publication date: 23 September 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2963

zbMATH Keywords

finite difference operatorsmeshhyperbolicity preservers

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Difference operators (39A70) Real polynomials: location of zeros (26C10)

Related Items (7)

Analytic closure of sets of real hyperbolic polynomials with separated roots ⋮ Linear 𝑞-difference, difference and differential operators preserving some 𝒜-entire functions ⋮ Suffridge's convolution theorem for polynomials and entire functions having only real zeros ⋮ Linear finite difference operators preserving the Laguerre–Pólya class ⋮ Hermite-Poulain theorems for linear finite difference operators ⋮ Connecting the \(q\)-multiplicative convolution and the finite difference convolution ⋮ Problems around polynomials: the good, the bad and the ugly\dots

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