Abstract:
The problem of optimal recovery, on the basis of exact or erroneous information, of symmetry-preserving operators on sets of elements of convolution type is solved. Using the information operator and a generating kernel, an approximation apparatus is constructed, called information-kernel splines. In particular cases, it coincides with sets of polynomial splines in one or several variables. Interpolation and smoothing are solvable for it.
\Bibitem{Zhe93}
\by A.~A.~Zhensykbaev
\paper Spline approximation and optimal recovery of operators
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 80
\issue 2
\pages 393--409
\mathnet{http://mi.mathnet.ru/eng/sm1029}
\crossref{https://doi.org/10.1070/SM1995v080n02ABEH003530}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1254802}
\zmath{https://zbmath.org/?q=an:0829.41010}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995QR47400007}
Linking options:
https://www.mathnet.ru/eng/sm1029
https://doi.org/10.1070/SM1995v080n02ABEH003530
https://www.mathnet.ru/eng/sm/v184/i12/p3
This publication is cited in the following 4 articles:
V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126
Zhensykbaev A., “Recovery of Operators on the Classes of Function with Restrictions in Integral Norms”, Dokl. Akad. Nauk, 351:6 (1996), 735–737
D. B. Bazarkhanov, “Approximation of certain classes of smooth periodic functions of several variables by means of interpolation splines defined over a uniform net”, Math. Notes, 57:6 (1995), 646–648
A. A. Zhensykbaev, “Nonlinear interpolation and norm minimization”, Math. Notes, 58:4 (1995), 1033–1041
Citation in format AMSBIB
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