Výsledky vyhledávání - "Komarov, Mikhail"

Akademický článek

Rate of interpolation of analytic functions with regularly decreasing coefficients by simple partial fractions

Publikováno v: Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 23, Iss 2, Pp 157-168 (2023)

We consider the problems of multiple interpolation of analytic functions $f(z)=f_0+f_1z+\dots$ in the unit disk with node $z=0$ by means of simple partial fractions (logarithmic derivatives of algebraic polynomials) with free poles and with all poles

Externí odkaz: https://doaj.org/article/cafed1e05e55458cac8d12c8f545fd67

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On reverse Markov-Nikol'skii inequalities for polynomials with restricted zeros

Autor: Komarov, Mikhail A.

Let $\Pi_n$ be the class of algebraic polynomials $P$ of degree $n$, all of whose zeros lie on the segment $[-1,1]$. In 1995, S.P. Zhou has proved the following Tur\'{a}n type reverse Markov-Nikol'skii inequality: $\|P'\|_{L_p[-1,1]}>c\, {(\sqrt{n})}

Externí odkaz: http://arxiv.org/abs/2405.19158

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

Autor: Komarov, Mikhail A.

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 $g_n(z)=(z-z_{1})^{-1}+\dots+(z-z_{n})^{-1}$, $|z_1|=\dots=|z_n|=1$. For any $p>0$, we establish the bou

Externí odkaz: http://arxiv.org/abs/2209.06689

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

Autor: Komarov, Mikhail A.

Publikováno v: Indagationes Mathematicae, 2020

Let $\alpha_{n1},\dots,\alpha_{nn}$ be the zeros of the $n$th Bessel polynomial $y_n(z)$ and let $a_{nk}=1-\alpha_{nk}/2$, $b_{nk}=1+\alpha_{nk}/2$ $(k=1,\dots,n)$. We propose the new formula \[z f'(z)\approx \sum_{k=1}^n \big(f(a_{nk} z)-f(b_{nk} z)

Externí odkaz: http://arxiv.org/abs/1911.05984

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Akademický článek

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Caratheodory type representation with unit weights and related approximation problems

Autor: Komarov, Mikhail A.

For arbitrary $n$ complex numbers $a_{\nu-1}$, $\nu=1,\dots,n$, where $n$ is sufficiently large, we get the representation in the form of power sums: $a_{\nu-1}=\lambda_1^\nu+\dots+\lambda_{2n+1}^\nu$, where $\lambda_k$ are distinct points, such that

Externí odkaz: http://arxiv.org/abs/1807.06499

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

Autor: Komarov, Mikhail A.

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 zeros lie on the unit circle $C:|z|=1$.

Externí odkaz: http://arxiv.org/abs/1804.08918

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