Optimal Recovery of a Derivative of an Analytic Function from Values of the Function Given with an Error on a Part of the Boundary. II

被引：1

作者：

Akopyan, R. R. ^{[1
,2
]}

机构：

[1] Ural Fed Univ, Inst Nat Sci & Math, Pr Lenina 51, Ekaterinburg 620000, Russia

[2] Russian Acad Sci, Krasovskii Inst Math & Mech, Ural Branch, S Kovalevskaya Str 16, Ekaterinburg 620990, Russia

来源：

ANALYSIS MATHEMATICA | 2020年 / 46卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

best approximation of an unbounded functional by bounded functionals; optimal recovery of a functional; analytic function;

D O I：

10.1007/s10476-020-0039-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We continue the study of several related extremal problems for functions analytic in a simply connected domainGwith a rectifiable Jordan boundary Gamma. In particular, the problem of optimal recovery of a derivative at a pointz(0)is an element of Gfrom limit boundary values given with an error on a measurable part gamma(1)of the boundary Gamma for the classQof functions with limit boundary values bounded by 1 on gamma(0)=Gamma gamma(1)as well as the problem of the best approximation of the derivative at a pointz(0)is an element of Gby bounded linear functionals inL(infinity)(gamma(1)) on the classQ. Complete exact solutions of the considered problems are obtained.

引用

页码：409 / 424

页数：16

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