The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space Lq

Abstract

The order estimates of the best M-term trigonometric approximations of functions \( {D}_{\beta}^{\psi } \) and the classes of (ψ , β)-differentiable periodic multivariate functions in the space L_q, 2 ≤ q < ∞ are obtained. It is shown that, under certain conditions imposed on the parameter q; the best M-term trigonometric approximations \( {e}_M{\left({L}_{\beta, 1}^{\psi}\right)}_q \) have better order than the best orthogonal trigonometric approximations \( e\frac{1}{M}{\left({L}_{\beta, 1}^{\psi}\right)}_q \).