Abstract:
The informativeness of all the linear functionals in
the recovery of functions in the classes Hωp is investigated.
The optimal recovery orders of functions in Hωp
are found. These are completely determined by embedding theorems,
similarly to the case of function classes with smoothness described
in terms of numerical parameters.
Bibliography: 28 titles.
Citation:
Sh. U. Azhgaliev, N. Temirgaliev, “Informativeness of all the linear functionals in the recovery of
functions in the classes Hωp”, Sb. Math., 198:11 (2007), 1535–1551
\Bibitem{AzhTem07}
\by Sh.~U.~Azhgaliev, N.~Temirgaliev
\paper Informativeness of all the linear functionals in the recovery of
functions in the classes $H_p^\omega$
\jour Sb. Math.
\yr 2007
\vol 198
\issue 11
\pages 1535--1551
\mathnet{http://mi.mathnet.ru/eng/sm1437}
\crossref{https://doi.org/10.1070/SM2007v198n11ABEH003895}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2374382}
\zmath{https://zbmath.org/?q=an:1138.41009}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000253636300001}
\elib{https://elibrary.ru/item.asp?id=9578641}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-40749151513}
Linking options:
https://www.mathnet.ru/eng/sm1437
https://doi.org/10.1070/SM2007v198n11ABEH003895
https://www.mathnet.ru/eng/sm/v198/i11/p3
This publication is cited in the following 7 articles:
A. B. Utesov, “Optimal Recovery of Functions from Numerical Information on Them and Limiting Error of the Optimal Computing Unit”, Math. Notes, 111:5 (2022), 759–767
Azhgaliyev Sh., Abikenova Sh., “On the Lower Bound in the Problem of Approximate Reconstruction of Functions By Values of the Radon Transform”, Vestn. Tomsk. Gos. Univ.-Mat. Mek., 2020, no. 66, 24–34
N. Temirgaliev, K. E. Sherniyazov, M. E. Berikhanova, “Exact Orders of Computational (Numerical) Diameters in Problems of Reconstructing Functions and Sampling Solutions of the Klein–Gordon Equation from Fourier Coefficients”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S165–S191
N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems”, Russian Math. (Iz. VUZ), 54:3 (2010), 45–62
Sh. K. Abikenova, N. Temirgaliev, “On the sharp order of informativeness of all possible linear functionals in the discretization of solutions of the wave equation”, Differ. Equ., 46:8 (2010), 1211–1214
I. Zh. Ibatulin, N. Temirgaliev, “On the informative power of all possible linear functionals for the discretization of solutions of the Klein-Gordon equation in the metric of L2,∞”, Differ. Equ., 44:4 (2008), 510–526
B. V. Simonov, S. Yu. Tikhonov, “Embedding theorems in constructive approximation”, Sb. Math., 199:9 (2008), 1367–1407
Citation in format AMSBIB
Contact us: