Best M-term trigonometric approximations of the classes $ B^{\Omega }_{{p,{\text{ $ \theta $ }}}} $ of periodic functions of many variables in the space L q

Abstract

We obtain order estimates for the best M-term trigonometric approximations of the classes B p, θ Ω of periodic functions of many variables in the space L q for several values of the parameters p and q.

Best M-Term trigonometric approximations of the classes $$ B_{p,\theta }^\Omega $$ of periodic functions of many variables

“…Therefore, setting d = 1 in (2), we obtain exact order estimates for e B M p q , θ Ω ( ) ; under certain conditions on the parameters p and q, these estimates were obtained in [17][18][19]. Moreover, estimate (2) also gives new results in the one-dimensional case for p = ∞, 1 ≤ q < ∞ and 1 ≤ p ≤ ∞, q = 1.…”

Best bilinear approximations of the classes $ S_{p,\theta }^\Omega B $ of periodic functions of many variables

“…In particular, the behavior of quantity (8) for some classes of functions of many variables was studied in [9,10] (see also the references therein). Also note that the behavior of the quantities of the best M -term approximation of the classes S p;Â B considered in the present paper was investigated in [11][12][13].…”

“…As in the previous theorem, we establish the upper bounds by using the estimates for e M .S p;Â B/ obtained in [12,13].…”