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Mat. Zametki, 2013, Volume 94, Issue 3, Pages 401–415 (Mi mz8892)  

This article is cited in 2 scientific papers (total in 2 papers)

Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev

Abstract: Order-sharp estimates of the best orthogonal trigonometric approximations of the Nikolskii–Besov classes $B^{r}_{p,\theta}$ of periodic functions of several variables in the space $L_{q}$ are obtained. Also the orders of the best approximations of functions of $2d$ variables of the form $g(x,y)=f(x-y)$, $x,y\in \mathbb{T}^d=\prod_{j=1}^{d}[-\pi,\pi]$, $f(x)\in B^r_{p,\theta}$, by linear combinations of products of functions of $d$ variables are established.

Keywords: best trigonometric approximation of functions, best bilinear approximation of functions, Nikolskii–Besov class of periodic functions, the space $L_{q}$, Fourier sum, Vallée-Poussin kernel, Minkowski inequality.

DOI: https://doi.org/10.4213/mzm8892

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English version:
Mathematical Notes, 2013, 94:3, 379–391

Bibliographic databases:

UDC: 517.51
Received: 13.07.2010
Revised: 05.07.2012

Citation: A. S. Romanyuk, “Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables”, Mat. Zametki, 94:3 (2013), 401–415; Math. Notes, 94:3 (2013), 379–391

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. A. Bekmaganbetov, Ye. Toleugazy, “Order of the orthoprojection widths of the anisotropic Nikol'skii–Besov classes in the anisotropic Lorentz space”, Eurasian Math. J., 7:3 (2016), 8–16  mathnet  mathscinet
    2. A. S. Romanyuk, V. S. Romanyuk, “Estimation of the best linear approximations for the classes $B_{\mathrm{p},\theta}^{\mathrm{r}}$ and singular numbers of the integral operators”, Ukr. Math. J., 68:9 (2017), 1424–1436  crossref  isi  scopus
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