Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables
Abstract
We obtain exact order estimates for the best $M$-term trigonometric approximations of the Besov classes $B_{∞,θ}^r$ in the space $L_q$. We also determine the exact orders of the best bilinear approximations of the classes of functions of $2d$ variables generated by functions of d variables from the classes $B_{∞,θ}^r$ with the use of translation of arguments.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 4, pp 612-629.
Citation Example: Romanyuk A. S., Romanyuk V. S. Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables // Ukr. Mat. Zh. - 2010. - 62, № 4. - pp. 536–551.
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