M. Komarov

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20182022

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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

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

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…

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

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