Abstract
We consider the problem of analytic continuation with inaccurate data from a finite subset U of a domain D of C n to a point z 0∈D U for the functions f belonging to a bounded correctness set V in a Hilbert space H(D) of analytic functions in D. In the case when H(D) is a Hilbert space with a reproducing kernel, we find constructive formulas for calculating the optimal error, the optimal function, and the optimal linear algorithm for extrapolation to a point z 0 for functions in V whose approximate values are given on a set U. Moreover, we study the asymptotics of the optimal error in the case when the errors of initial data vanish.
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Maergoiz, L.S., Fedotov, A.M. Optimal Error of Analytic Continuation from a Finite Set with Inaccurate Data in Hilbert Spaces of Holomorphic Functions. Siberian Mathematical Journal 42, 926–935 (2001). https://doi.org/10.1023/A:1011967711386
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DOI: https://doi.org/10.1023/A:1011967711386