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Ural Math. J., 2017, Volume 3, Issue 2, Pages 6–13 (Mi umj37)  

This article is cited in 1 scientific paper (total in 1 paper)

Approximation of the differentiation operator on the class of functions analytic in an annulus

Roman R. Akopyanab

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University, Ekaterinburg

Abstract: In the class of functions analytic in the annulus $C_r:=ż\in\mathbb{C}  :  r<|z|<1\}$ with bounded $L^p$-norms on the unit circle, we study the problem of the best approximation of the operator taking the nontangential limit boundary values of a function on the circle $\Gamma_r$ of radius $r$ to values of the derivative of the function on the circle $\Gamma_\rho$ of radius $\rho,  r<\rho<1,$ by bounded linear operators from $L^p(\Gamma_r)$ to $L^p(\Gamma_ \rho)$ with norms not exceeding a number $N$. A solution of the problem has been obtained in the case when $N$ belongs to the union of a sequence of intervals. The related problem of optimal recovery of the derivative of a function from boundary values of the function on $\Gamma_\rho$ given with an error has been solved.

Keywords: Best approximation of operators, Optimal recovery, Analytic functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02705
Ministry of Education and Science of the Russian Federation 9356.2016.1
02.A03.21.0006
This work was supported by the Russian Foundation for Basic Research (project no. 15-01-02705), the Program for State Support of Leading Scientific Schools of the Russian Federation (project no. NSh-9356.2016.1), and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).


DOI: https://doi.org/10.15826/umj.2017.2.002

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Citation: Roman R. Akopyan, “Approximation of the differentiation operator on the class of functions analytic in an annulus”, Ural Math. J., 3:2 (2017), 6–13

Citation in format AMSBIB
\Bibitem{Ako17}
\by Roman~R.~Akopyan
\paper Approximation of the differentiation operator on the class of functions analytic in an annulus
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 2
\pages 6--13
\mathnet{http://mi.mathnet.ru/umj37}
\crossref{https://doi.org/10.15826/umj.2017.2.002}


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    This publication is cited in the following articles:
    1. V. V. Arestov, “Nailuchshee ravnomernoe priblizhenie operatora differentsirovaniya ogranichennymi v prostranstve $L_2$ operatorami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 34–56  mathnet  crossref  elib
  • Ural Mathematical Journal
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