338 citations
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math.CA2019★ 1 cited
Hermite-Poulain theorems for linear finite difference operators
Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova
We establish analogues of the Hermite-Poulain theorem for linear finite difference operators with constant coefficients defined on sets of polynomials with roots on a straight line…
math.CA2016★ 2 cited
Linear finite difference operators preserving Laguerre-Pólya class
O. Katkova, M. Tyaglov, A. Vishnyakova
We completely describe all finite difference operators of the form preserving the Laguerre-Pólya class of entire functions…