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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 247–257 (Mi timm1047)  

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

Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables

S. A. Stasyuk

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev

Abstract: We obtain exact order estimates for approximations of mixed smoothness classes $\mathbf{MB}^\Omega_{p,\theta}$ by Fourier sums in the metric $L_q$ for $1<p<q<\infty$. The spectrum of approximation polynomials lies in the sets generated by level surfaces of the function $\Omega(t)/\prod_{j=1}^dt_j^{1/p-1/q}$. Under some matching conditions on the parameters $p,q$ and $\theta$, we obtain exact order estimates for Kolmogorov widths of the classes under consideration in the metric $L_q$.

Keywords: hyperbolic cross, Kolmogorov width, best approximation, mixed smoothness, Fourier sums.

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Bibliographic databases:

Document Type: Article
UDC: 517.51
Received: 16.10.2013

Citation: S. A. Stasyuk, “Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 247–257

Citation in format AMSBIB
\Bibitem{Sta14}
\by S.~A.~Stasyuk
\paper Approximation by Fourier sums and Kolmogorov widths for classes $\mathbf{MB}^\Omega_{p,\theta}$ of periodic functions of several variables
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 1
\pages 247--257
\mathnet{http://mi.mathnet.ru/timm1047}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364209}
\elib{http://elibrary.ru/item.asp?id=21258500}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sh. A. Balgimbaeva, T. I. Smirnov, “Otsenki poperechnikov Fure klassov periodicheskikh funktsii so smeshannym modulem gladkosti”, Tr. IMM UrO RAN, 21, no. 4, 2015, 78–94  mathnet  mathscinet  elib
    2. Stasyuk S.A., Yanchenko S.Ya., “Approximation of Functions From Nikolskii-Besov Type Classes of Generalized Mixed Smoothness”, Anal. Math., 41:4 (2015), 311–334  crossref  mathscinet  zmath  isi  elib  scopus
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