2017
Том 69
№ 7

All Issues

Approximative characteristics of the isotropic classes of periodic functions of many variables

Romanyuk A. S.

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Abstract

Exact-order estimates are obtained for the best orthogonal trigonometric approximations of the Besov $(B_{p,θ}^r)$ and Nukol’skii $(H_p^r )$ classes of periodic functions of many variables in the metric of $L_q , 1 ≤ p, q ≤ ∞$. We also establish the orders of the best approximations of functions from the same classes in the spaces $L_1$ and $L_{∞}$ by trigonometric polynomials with the corresponding spectrum.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 4, pp 613-626.

Citation Example: Romanyuk A. S. Approximative characteristics of the isotropic classes of periodic functions of many variables // Ukr. Mat. Zh. - 2009. - 61, № 4. - pp. 513-523.

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