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A problem of Heins and optimal extrapolation of analytic functions given with an error. (Russian) Zbl 0578.30034

Let B be the class of analytic functions on the unit circle that are bounded in module by one. The following extremal problem posed by M. Heins is studied: to find the value \(\sup \{| f(z_ 0)|: f\in B,| f(z)| \leq \delta,z\in [a,b]\}\) or its order, where [a,b]\(\subset [-1,1]\), \(z_ 0\in (b,1)\), \(\delta\in (0,1)\), and the extremal function. A general solution is given.

MSC:

30E99 Miscellaneous topics of analysis in the complex plane
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