2 papers
math.CV2025
Convolution operators preserving the set of totally positive sequences
Olga Katkova, Anna Vishnyakova
A real sequence is called {\it totally positive} if all minors of the infinite Toeplitz matrix are nonnegative (he…
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 \…