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arXiv · 2410.12448

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

K. V. Pozharska·A. S. Romanyuk·S. Ya. Yanchenko
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Abstract

We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ of periodic functions of many variables with a bounded dominating mixed derivative. The approximation is made using trigonometric polynomials with the spectrum in step-hyperbolic crosses, and the error is estimated in the metric of the space $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$.

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K. V. Pozharska, A. S. Romanyuk, S. Ya. Yanchenko. 2024-10-16. Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative. https://doi.org/10.3842/umzh.v76i7.8307

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