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

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 polyno...

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Bibliographic Details
Date:2024
Main Authors: Pozharska, K., Romanyuk , A., Yanchenko, S., Пожарська, Катерина, Романюк, Анатолій, Янченко, Сергій
Format: Article
Language:Ukrainian
Published: Institute of Mathematics, NAS of Ukraine 2024
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/8307
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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Summary: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 $B_{q,1}(\mathbb{T}^d),$ $1 \leq p, q < \infty.$
DOI:10.3842/umzh.v76i7.8307