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math.CV2024
On the number of real zeroes of a homogeneous differential polynomial and a generalization of the Hawaii conjecture
Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova
For a given real polynomial we study the possible number of real roots of a differential polynomial $H_{\varkappa}[p](x) = \varkappa\left(p'(x)\right)^2-p(x)p''(x), \varkappa \…
math.CV2018
Linear finite difference operators with constant coefficients and distribution of zeros of polynomials
Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova
We study the effect of finite difference operators of finite order on the distribution of zeros of polynomials and entire functions.