OPTIMAL RECOVERY OF A DERIVATIVE OF AN ANALYTIC FUNCTION FROM VALUES OF THE FUNCTION GIVEN WITH AN ERROR ON A PART OF THE BOUNDARY

被引：5

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 | 2018年 / 44卷 / 01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; HARDY-APPROXIMATION; OPERATORS; SUBSETS; CIRCLE;

D O I：

10.1007/s10476-018-0102-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study several related extremal problems for functions analytic in a simply connected domain G with a rectifiable Jordan boundary Gamma, in particular, the problem of optimal recovery of the derivative at a point z(0) is an element of G from limit boundary values given with an error on a measurable part gamma(1) of the boundary Gamma for the class Q of 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 point z(0) is an element of G by bounded linear functionals in L-infinity(gamma(1)) on the class Q.

引用

页码：3 / 19

页数：17

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