2018
Том 70
№ 9

# Approximation of the Classes $H_p^{Ω}$ of Periodic Functions of Many Variables in the Space $L_p$

Derev’yanko N. V.

Abstract

We establish upper estimates for the approximation of the classes $H_p^{Ω}$ of periodic functions of many variables by polynomials constructed by using the system obtained as the tensor product of the systems of functions of one variable. These results are then used to establish the exact-order estimates of the orthoprojective widths for the classes $H_p^{Ω}$ in the space $L_p$ with $p ∈ \{1, ∞\}$.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 5, pp 707-718.

Citation Example: Derev’yanko N. V. Approximation of the Classes $H_p^{Ω}$ of Periodic Functions of Many Variables in the Space $L_p$ // Ukr. Mat. Zh. - 2014. - 66, № 5. - pp. 634–644.

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