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Approximation of classes of periodic functions of several variables. (English. Russian original) Zbl 1020.42012

Math. Notes 71, No. 1, 98-109 (2002); translation from Mat. Zametki 71, No. 1, 109-121 (2002).
Summary: We study the approximation of the classes \(B^r_{p,\theta}\) and \(W^r_{p,\alpha}\) of periodic functions of several variables by multiple Fourier sums of fixed order constructed with regard to individual properties of functions from these classes. In a number of cases, such approximations allow us to achieve a better degree of approximation of the classes indicated above as compared to their approximation by staircase hyperbolic Fourier sums.

MSC:

42B99 Harmonic analysis in several variables
42A10 Trigonometric approximation
41A25 Rate of convergence, degree of approximation
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