M. Komarov

activity

20152022

z f^{'} (z)

by special sums associated with the zeros of the Bessel polynomials

3 citations · 6 across the 5 of their papers we have counts for

collaborators

5 papers

math.CA2022

A Newman type bound for $L_{p} [- 1, 1]$ -means of the logarithmic derivative of polynomials having all zeros on the unit circle

Mikhail A. Komarov

Let $g_{n}$ , $n = 1, 2, \dots$ , be the logarithmic derivative of a complex polynomial having all zeros on the unit circle, i.e., a function of the form $g_n(z)=(z-z_{1})^{-1}+\dots+(z-z_…

math.CA2019★ 3 cited

Rate of approximation of $z f^{'} (z)$ by special sums associated with the zeros of the Bessel polynomials

Mikhail A. Komarov

Let $α_{n 1}, \dots, α_{nn}$ be the zeros of the $n$ th Bessel polynomial $y_{n} (z)$ and let $a_{nk} = 1 - α_{nk} /2$ , $b_{nk} = 1 + α_{nk} /2$ $(k = 1, \dots, n)$ . We propose the new formula \[z f'(z…

math.CA2018★ 1 cited

Caratheodory type representation with unit weights and related approximation problems

Mikhail A. Komarov

For arbitrary $n$ complex numbers $a_{ν - 1}$ , $ν = 1, \dots, n$ , where $n$ is sufficiently large, we get the representation in the form of power sums: $a_{ν - 1} = λ_{1}^{ν} + \dots + λ_{2 n + 1}^{ν}$ ,…

math.CA2018

Rate of approximation by logarithmic derivatives of polynomials whose zeros lie on a circle

Mikhail A. Komarov

We obtain an estimate for uniform approximation rate of bounded analytic in the unit disk functions by logarithmic derivatives of $C$ -polynomials, i.e., polynomials, all of whose z…

math.CA2015★ 2 cited

Extremal and approximation properties of simple partial fractions

V. I. Danchenko, M. A. Komarov, P. V. Chunaev

In approximation theory, logarithmic derivatives of complex polynomials are called simple partial fractions (SPF) as suggested by Eu.P. Dolzhenko. Many solved and unsolved extremal…

A Newman type bound for Lp​[−1,1]-means of the logarithmic derivative of polynomials having all zeros on the unit circle

Rate of approximation of zf′(z) by special sums associated with the zeros of the Bessel polynomials

Caratheodory type representation with unit weights and related approximation problems

Rate of approximation by logarithmic derivatives of polynomials whose zeros lie on a circle

Extremal and approximation properties of simple partial fractions

A Newman type bound for $L_{p} [- 1, 1]$ -means of the logarithmic derivative of polynomials having all zeros on the unit circle

Rate of approximation of $z f^{'} (z)$ by special sums associated with the zeros of the Bessel polynomials