O. Katkova

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math.CV2025

Convolution operators preserving the set of totally positive sequences

Olga Katkova, Anna Vishnyakova

A real sequence $(a_{k})_{k = 0}^{\infty}$ is called {\it totally positive} if all minors of the infinite Toeplitz matrix $∥ a_{j - i} ∥_{i, j = 0}^{\infty}$ 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 $p$ 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 \…