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

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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Document Type: Article
UDC: 517.51

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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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
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
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