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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.

Reviewer: Yusuf Avci (Istanbul)

### 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 |

### Keywords:

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

Zbl 1413.30002
Full Text:
DOI

### References:

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