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Best approximations and widths of classes of periodic functions of several variables. (English. Russian original) Zbl 1173.41012
Sb. Math. 199, No. 2, 253-275 (2008); translation from Mat. Sb. 199, No. 2, 93-114 (2008).
The author computes estimates for the order of best approximation of Besov classes of periodic functions of severable variables. The approximations are by an appropriate restricted class of trigonometric polynomials. The estimates are computed for both the uniform norm and for approximation in the mean. Linear widths are also computed for the \(L_1\)-norm.

MSC:
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A45 Approximation by arbitrary linear expressions
41A50 Best approximation, Chebyshev systems
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