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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 \(q\).

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
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