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

We continue the study of several related extremal problems for functions analytic in a simply connected domain G with a rectifiable Jordan boundary Γ. In particular, the problem of optimal recovery of a derivative at a point z 0 ∈ G from limit boundary values given with an error on a measurable part...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2020-09, Vol.46 (3), p.409-424
Main Author: Akopyan, R. R.
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Boundary value problems
Error analysis
Exact solutions
Mathematical analysis
Mathematics
Mathematics and Statistics
Recovery
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Summary:We continue the study of several related extremal problems for functions analytic in a simply connected domain G with a rectifiable Jordan boundary Γ. In particular, the problem of optimal recovery of a derivative at a point z 0 ∈ G from limit boundary values given with an error on a measurable part γ 1 of the boundary Γ for the class Q of functions with limit boundary values bounded by 1 on γ 0 = Γ γ 1 as well as the problem of the best approximation of the derivative at a point z 0 ∈ G by bounded linear functionals in L ∞ (γ 1 ) on the class Q . Complete exact solutions of the considered problems are obtained.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-020-0039-5