This article is cited in 6 scientific papers (total in 6 papers)
Approximation of periodic functions of several variables with bounded mixed difference
V. N. Temlyakov
This paper studies questions concerning the approximation of functions of several variables by trigonometric polynomials whose harmonics lie in a “hyperbolic cross” and also properties of functions which do not have harmonics lying in a “hyperbolic cross”. Analogues of H. Bohr's inequality are obtained for such functions. Estimates of optimal order are obtained for the upper bounds of best approximations of certain classes of functions, defined using mixed differences, by trigonometric polynomials whose harmonics lie in a “hyperbolic cross”. The diameters of certain classes are found.
Bibliography: 13 titles.
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Mathematics of the USSR-Sbornik, 1982, 41:1, 53–66
V. N. Temlyakov, “Approximation of periodic functions of several variables with bounded mixed difference”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 65–80; Math. USSR-Sb., 41:1 (1982), 53–66
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\paper Approximation of periodic functions of several variables with bounded mixed difference
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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V. N. Temlyakov, “Approximation of functions with a bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions”, Math. USSR-Izv., 20:1 (1983), 173–187
V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions”, Math. USSR-Izv., 27:2 (1986), 285–322
V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Math. USSR-Izv., 28:1 (1987), 133–150
È. M. Galeev, “Order estimates of smallest norms, with respect to the choice of $N$ harmonics, of derivatives of the Dirichlet and Favard kernels”, Math. USSR-Sb., 72:2 (1992), 567–578
G. Akishev, “O poryadkakh priblizheniya klassov gladkikh funktsii v prostranstvakh Lebega so smeshannoi normoi”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 148, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2006, 5–17
Temlyakov V., “on the Entropy Numbers of the Mixed Smoothness Function Classes”, J. Approx. Theory, 217 (2017), 26–56
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