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This article is cited in 4 scientific papers (total in 4 papers)
Approximation of periodic functions of several variables by bilinear forms
V. N. Temlyakov
Abstract:
The orders of the quantities
$$
\tau_M(F)_{p_1,p_2}=\sup_{f\in F}\inf_{\substack{u_i(\mathbf x),v_i(\mathbf y)
i=1,…,M}}\|f(\mathbf x-\mathbf y)-\sum_{i=1}^Mu_i(\mathbf x)v_i(\mathbf y)\|_{p_1,p_2}
$$
are obtained, where $F$ is a class of functions with mixed derivative, or the corresponding prelimiting difference, bounded in $L_q$. In the process some results of independent interest are obtained: a generalization of the Hardy–Littlewood theorem, and the orders of the best $M$-term trigonometric approximations.
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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 133–150
Bibliographic databases:
 
UDC:
517.5
MSC: 42B05, 41A63, 41A17
Received: 24.02.1983
Citation:
V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 137–155; Math. USSR-Izv., 28:1 (1987), 133–150
Citation in format AMSBIB
\Bibitem{Tem86}
\by V.~N.~Temlyakov
\paper Approximation of periodic functions of several variables by bilinear forms
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 1
\pages 137--155
\mathnet{http://mi.mathnet.ru/izv1474}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=835569}
\zmath{https://zbmath.org/?q=an:0651.42002|0607.42003}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 1
\pages 133--150
\crossref{https://doi.org/10.1070/IM1987v028n01ABEH000870}
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This publication is cited in the following articles:
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Jan Schneider, “Error estimates for two-dimensional cross approximation”, Journal of Approximation Theory, 162:9 (2010), 1685
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V. N. Temlyakov, “Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness”, Sb. Math., 206:11 (2015), 1628–1656
    -
Temlyakov V., “Sparse Approximation by Greedy Algorithms”, Mathematical Analysis, Probability and Applications – Plenary Lectures, Springer Proceedings in Mathematics & Statistics, Springer Proceedings in Mathematics & Statistics, 177, ed. Qian T. Rodino L., Springer, 2016, 183–215
 -
Temlyakov V., “Constructive Sparse Trigonometric Approximation For Functions With Small Mixed Smoothness”, Constr. Approx., 45:3 (2017), 467–495
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