Romanyuk, A. S. 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. Cited in 1 ReviewCited in 7 Documents MSC: 42B99 Harmonic analysis in several variables 42A10 Trigonometric approximation 41A25 Rate of convergence, degree of approximation Keywords:orthogonal trigonometric approximation; Besov class of functions; Rudin-Shapiro polynomials; several variables; multiple Fourier sums; degree of approximation; staircase hyperbolic Fourier sums PDFBibTeX XMLCite \textit{A. S. Romanyuk}, Math. Notes 71, No. 1, 98--109 (2002; Zbl 1020.42012); translation from Mat. Zametki 71, No. 1, 109--121 (2002) Full Text: DOI