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Sibirskii Matematicheskii Zhurnal, 1993, Volume 34, Number 3, Pages 144–160
(Mi smj1661)
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This article is cited in 2 scientific papers (total in 2 papers)
On some problems of optimal recovery of analytic and harmonic functions from inaccurate data
K. Yu. Osipenko, M. I. Stesin
Abstract:
Some general theorems on optimal recovery are proved which are then applied to solving recovery problems in the Hardy $H_p$ and Bergman $A_p$ spaces as well as in the analogous spaces of harmonic functions. In particular, we obtain a generalization of the Schwartz lemma for these spaces. For the space $H_p$, we solve the problem of finding an optimal formula for numeric differentiation which uses the values, known to within an error $\delta$, of functions at the points $-h$ and $h$. For any fixed $\delta$ and $p=\infty$, we find the optimal value of $h$.
Received: 10.05.1990
Citation:
K. Yu. Osipenko, M. I. Stesin, “On some problems of optimal recovery of analytic and harmonic functions from inaccurate data”, Sibirsk. Mat. Zh., 34:3 (1993), 144–160; Siberian Math. J., 34:3 (1993), 523–539
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https://www.mathnet.ru/eng/smj1661 https://www.mathnet.ru/eng/smj/v34/i3/p144
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Abstract page: | 220 | Full-text PDF : | 106 |
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