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Sibirsk. Mat. Zh., 2016, Volume 57, Number 2, Pages 469–478 (Mi smj2758)  

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

Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$

M. Sh. Shabozova, G. A. Yusupovb

a Juraev Institute of Mathematics, Tajik Academy of Sciences, Dushanbe, Tajikistan
b Tajik National University, Dushanbe, Tajikistan

Abstract: We compute the exact values of widths for various widths for the classes $W_{q,a}^{(r)}(\Phi,\mu)$, $\mu\ge1$, of analytic functions in the disk belonging to the Hardy space $H_q$, $q\ge1$, whose averaged moduli of continuity of the boundary values of the derivatives with respect to the argument $f_a^{(r)}$, $r\in\mathbb N$, are dominated by a given function $\Phi$. For calculating the linear and Gelfand $n$-widths, we use best linear approximation for these functions.

Keywords: best linear approximation method, modulus of continuity, Hardy space, majorant, $n$-width.

DOI: https://doi.org/10.17377/smzh.2016.57.219

Full text: PDF file (429 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:2, 369–376

Bibliographic databases:

UDC: 517.5
Received: 31.03.2015

Citation: M. Sh. Shabozov, G. A. Yusupov, “Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$”, Sibirsk. Mat. Zh., 57:2 (2016), 469–478; Siberian Math. J., 57:2 (2016), 369–376

Citation in format AMSBIB
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\by M.~Sh.~Shabozov, G.~A.~Yusupov
\paper Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 2
\pages 469--478
\mathnet{http://mi.mathnet.ru/smj2758}
\crossref{https://doi.org/10.17377/smzh.2016.57.219}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3510207}
\elib{https://elibrary.ru/item.asp?id=26237282}
\transl
\jour Siberian Math. J.
\yr 2016
\vol 57
\issue 2
\pages 369--376
\crossref{https://doi.org/10.1134/S0037446616020191}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84969746019}


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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. M. Sh. Shabozov, M. S. Saidusainov, “Srednekvadraticheskoe priblizhenie funktsii kompleksnogo peremennogo summami Fure po ortogonalnym sistemam”, Tr. IMM UrO RAN, 25, no. 2, 2019, 258–272  mathnet  crossref  elib
    2. S. B. Vakarchuk, “Estimates of the Values of $n$-Widths of Classes of Analytic Functions in the Weight Spaces $H_{2,\gamma}(D)$”, Math. Notes, 108:6 (2020), 775–790  mathnet  crossref  crossref  mathscinet  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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