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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. (English) Zbl 1474.30004

This technical work is a continuation of the author [Anal. Math. 44, No. 1, 3–19 (2018; Zbl 1413.30002)]. In this paper, he completes the study of several extremal problems for functions analytic in a simply connected domain \(G\) with a rectifiable Jordan boundary curve \(\Gamma\) and obtains complete exact solutions of these problems. The paper consists of four parts. In Part 1, he describes the problems in question and introduces some notation necessary to state the results. Using the notation he builds up, he states the main results in Part 2. He obtains a special formula for the derivative of an analytic function in the Hardy class in Part 3 and then he proceeds to the proof of the main results in Part 4.

MSC:

30A10 Inequalities in the complex plane
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C85 Capacity and harmonic measure in the complex plane
30E10 Approximation in the complex plane

Citations:

Zbl 1413.30002
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References:

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