Найкращі наближення класів періодичних  функцій багатьох змінних  з обмеженою домінуючою мішаною похідною

Катерина Пожарська; Анатолій Романюк; Сергій Янченко

doi:10.3842/umzh.v76i7.8307

Authors

K. Pozharska Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv https://orcid.org/0000-0001-7599-8117
A. Romanyuk Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv https://orcid.org/0000-0002-6268-0799
S. Yanchenko Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv https://orcid.org/0000-0003-4906-3806

DOI:

https://doi.org/10.3842/umzh.v76i7.8307

Keywords:

Sobolev classes, best approximation, dominating mixed derivative, Fourier sums, step-hyperbolic cross

Abstract

UDC 517.51

We establish exact order estimates for approximations of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ of periodic functions of many variables with bounded dominant mixed derivative. The approximation is performed by using trigonometric polynomials with spectra in step hyperbolic crosses, and the error is estimated in the metric of the space $B_{q,1}(\mathbb{T}^d),$ $1 \leq p, q < \infty.$

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Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative

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