A. Vishnyakova

activity

20052026

most citedMultiplier sequences and logarithmic mesh

2 citations · 5 across the 21 of their papers we have counts for

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14 papers · 1 filter

math.CV2026

Polynomially Deformed Normalized Pochhammer Sequences Having Generating Functions With Only Real Non-positive Zeros

Anna Vishnyakova

For a given real number $a > 0$ and a given real polynomial $P_{n} \in R [x]$ of degree $n = 0, 1, 2, \dots$ it is easy to see that $ \sum_{k=0}^\infty \frac{(a)_k}{k!} P_n(k) z^…

math.CV2026

Polynomials interpolated totally positive sequences

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 (wh…

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 \…

math.CV2024

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…

math.CV2024

An analog of multiplier sequences for the set of totally positive sequences

Olga Katkova, Anna Vishnyakova

A real sequence $(b_{k})_{k = 0}^{\infty}$ is called totally positive if all minors of the infinite matrix $∥ b_{j - i} ∥_{i, j = 0}^{\infty}$ are nonnegative (here $b_{k} = 0$ for…