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Eurasian Math. J., 2010, Volume 1, Number 3, Pages 11–26 (Mi emj26)  

This article is cited in 4 scientific papers (total in 4 papers)

Estimates for the widths of classes of periodic functions of several variables – I

D. B. Bazarkhanov

Institute of Mathematics, Almaty, Kazakhstan

Abstract: We establish estimates sharp in order for the Kolmogorov and linear widths of the classes $\mathrm{B}^{s m}_{p q}( \mathbb{T}^k)$ and $\mathrm{L}^{s m}_{p q}( \mathbb{T}^k)$ of Nikol'skii–Besov, Lizorkin–Triebel types respectively, in the space $L_r(\mathbb{T}^k)$ for a certain range of the parameters $s,p,q,r$, and $m$.

Keywords and phrases: Kolmogorov width, linear width, function class, mixed smoothness, wavelet.

Full text: PDF file (438 kB)
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Bibliographic databases:
MSC: 41A46, 41A63, 42C40
Received: 19.08.2010
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Citation: D. B. Bazarkhanov, “Estimates for the widths of classes of periodic functions of several variables – I”, Eurasian Math. J., 1:3 (2010), 11–26

Citation in format AMSBIB
\Bibitem{Baz10}
\by D.~B.~Bazarkhanov
\paper Estimates for the widths of classes of periodic functions of several variables~--~I
\jour Eurasian Math. J.
\yr 2010
\vol 1
\issue 3
\pages 11--26
\mathnet{http://mi.mathnet.ru/emj26}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2904764}
\zmath{https://zbmath.org/?q=an:1216.41021}


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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. Toleugazy Y., “Embedding Theorems, Theorems of a Trace and Approach For Anisotropic B-PR(Alpha Q) (T-D) Nikol'Skii-Besov Spaces”, Bull. Karaganda Univ-Math., 84:4 (2016), 146–154  isi
    2. Van Kien Nguyen, “Gelfand Numbers of Embeddings of Mixed Besov Spaces”, J. Complex., 41 (2017), 35–57  crossref  isi
    3. D. B. Bazarkhanov, “Lineinoe vosstanovlenie psevdodifferentsialnykh operatorov na klassakh gladkikh funktsii na m-mernom tore. II”, Tr. IMM UrO RAN, 25, no. 4, 2019, 15–30  mathnet  crossref  elib
    4. V. I. Burenkov, T. V. Tararykova, “Necessary and sufficient conditions of compactness of certain embeddings of Sobolev spaces”, Eurasian Math. J., 10:4 (2019), 14–23  mathnet  crossref  mathscinet
  • Eurasian Mathematical Journal
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