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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 5, Pages 1106–1116
(Mi smj1408)
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This article is cited in 1 scientific paper (total in 1 paper)
Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions
L. S. Maergoiza, A. M. Fedotovb a Krasnoyarsk State Academy of Architecture and Construction
b Institute of Computing Technologies, Siberian Branch of the Russian Academy of Sciences
Abstract:
We consider the problem of analytic continuation with inaccurate data from a finite subset $U$ of a domain $D$ of $\mathbb{C}^n$ to a point $z_0\in D\setminus U$ функции $f$ из $H(D)$ 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
Received: 05.01.2001
Citation:
L. S. Maergoiz, A. M. Fedotov, “Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions”, Sibirsk. Mat. Zh., 42:5 (2001), 1106–1116; Siberian Math. J., 42:5 (2001), 926–935
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https://www.mathnet.ru/eng/smj1408 https://www.mathnet.ru/eng/smj/v42/i5/p1106
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