Romanyuk, A. S. Best \(M\)-term trigonometric approximations of Besov classes of periodic functions of several variables. (English. Russian original) Zbl 1066.42001 Izv. Math. 67, No. 2, 265-302 (2003); translation from Izv. Ross. Akad. Nauk Ser. Mat. 67, No. 2, 61-100 (2003). Summary: We obtain estimates of exact order for the best \(M\)-term trigonometric approximations of the Besov classes \(B^r_{p,\theta}\) of periodic functions of several variables in \(L_q\) with certain relations between \(p\) and \(q\). Cited in 17 Documents MSC: 42A10 Trigonometric approximation 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 41A50 Best approximation, Chebyshev systems Keywords:trigonometric approximation; periodic functions; Besov class PDFBibTeX XMLCite \textit{A. S. Romanyuk}, Izv. Math. 67, No. 2, 265--302 (2003; Zbl 1066.42001); translation from Izv. Ross. Akad. Nauk Ser. Mat. 67, No. 2, 61--100 (2003) Full Text: DOI