2 citations · 5 across the 11 of their papers we have counts for
11 papers
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…
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 \…
In search of Newton-type inequalities
Olga Katkova, Boris Shapiro, Anna Vishnyakova
In this paper, we prove a number of results providing either necessary or sufficient conditions guaranteeing that the number of real roots of real polynomials of a given degree is…
An analog of multiplier sequences for the set of totally positive sequences
Olga Katkova, Anna Vishnyakova
A real sequence is called totally positive if all minors of the infinite matrix are nonnegative (here for…
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…
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.