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Mat. Zametki, 2002, Volume 72, Issue 5, Pages 665–669 (Mi mz454)  

This article is cited in 7 scientific papers (total in 7 papers)

Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods

S. B. Vakarchuk

Ukrainian Academy of Customs

Abstract: In the Hardy space $H_{p,\rho }$ ($p\ge 1$, $0<\rho \le 1$, $H_{p,1}\equiv H_p$) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes $W(r,\Phi ,\mu )$ of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational $n$-widths of these classes.

DOI: https://doi.org/10.4213/mzm454

Full text: PDF file (178 kB)
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English version:
Mathematical Notes, 2002, 72:5, 615–619

Bibliographic databases:

UDC: 517.5
Received: 12.09.2001

Citation: S. B. Vakarchuk, “Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods”, Mat. Zametki, 72:5 (2002), 665–669; Math. Notes, 72:5 (2002), 615–619

Citation in format AMSBIB
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\by S.~B.~Vakarchuk
\paper Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 5
\pages 665--669
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\crossref{https://doi.org/10.4213/mzm454}
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\transl
\jour Math. Notes
\yr 2002
\vol 72
\issue 5
\pages 615--619
\crossref{https://doi.org/10.1023/A:1021496620022}
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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. S. B. Vakarchuk, M. Sh. Shabozov, “The widths of classes of analytic functions in a disc”, Sb. Math., 201:8 (2010), 1091–1110  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Vakarchuk S.B., Shabozov M.Sh., “On Widths of Classes of Analytic Functions on the Disk in Weight Banach Spaces”, Doklady Mathematics, 81:3 (2010), 426–428  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Shabozov M.Sh., Kholmamadova Sh.A., “O poperechnikakh nekotorykh klassov analiticheskikh v kruge funktsii”, Izvestiya tulskogo gosudarstvennogo universiteta. estestvennye nauki, 2012, no. 3, 48–59  elib
    4. M. Sh. Shabozov, G. A. Yusupov, “Best approximation methods and widths for some classes of functions in $H_{q,\rho}$, $1\le q\le\infty$, $0<\rho\le1$”, Siberian Math. J., 57:2 (2016), 369–376  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Langarshoev M.R., “On the Best Linear Methods of Approximation and the Exact Values of Widths for Some Classes of Analytic Functions in the Weighted Bergman Space”, Ukr. Math. J., 67:10 (2016), 1537–1551  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. Sh. Shabozov, M. R. Langarshoev, “Best linear approximation methods for some classes of analytic functions on the unit disk”, Siberian Math. J., 60:6 (2019), 1101–1108  mathnet  crossref  crossref  isi  elib
    7. 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
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