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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Pozharska, K. V., Romanyuk, A. S., Yanchenko, S. Ya.
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913548865634304
author Pozharska, K. V.
Romanyuk, A. S.
Yanchenko, S. Ya.
author_facet Pozharska, K. V.
Romanyuk, A. S.
Yanchenko, S. Ya.
contents We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbolα}(\mathbb{T}^d)$ 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 $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$.
format Preprint
id arxiv_https___arxiv_org_abs_2410_12448
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative
Pozharska, K. V.
Romanyuk, A. S.
Yanchenko, S. Ya.
Classical Analysis and ODEs
41A46, 42A10, 41A50
We established exact in order estimates an approximation of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbolα}(\mathbb{T}^d)$ 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 $B_{q,1}(\mathbb{T}^d)$, $1 \leqslant p, q < \infty$.
title Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative
topic Classical Analysis and ODEs
41A46, 42A10, 41A50
url https://arxiv.org/abs/2410.12448