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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 285–295 (Mi mz8049)  

This article is cited in 19 scientific papers (total in 19 papers)

Diameters of certain classes of analytic functions

L. V. Taikov

Moscow Institute of Forestry Engineering

Abstract: Exact values have been found, for the diameters in the sense of Kolmogorov of certain classes of functions with a Hardy metric, analytic in the unit circle, whose boundary values admit of a representation by a convolution or the averaged modulus of smoothness of their boundary values is majorized by a given function. In passing, certain extremal properties of trigonometric polynomials are established.

Full text: PDF file (675 kB)

English version:
Mathematical Notes, 1977, 22:2, 650–656

Bibliographic databases:

UDC: 517.5
Received: 06.02.1976

Citation: L. V. Taikov, “Diameters of certain classes of analytic functions”, Mat. Zametki, 22:2 (1977), 285–295; Math. Notes, 22:2 (1977), 650–656

Citation in format AMSBIB
\Bibitem{Tai77}
\by L.~V.~Taikov
\paper Diameters of certain classes of analytic functions
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 285--295
\mathnet{http://mi.mathnet.ru/mz8049}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=466567}
\zmath{https://zbmath.org/?q=an:0382.30026}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 650--656
\crossref{https://doi.org/10.1007/BF01780976}


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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, “Best linear methods of approximation and widths of classes of analytic functions in a disk”, Math. Notes, 57:1 (1995), 21–27  mathnet  crossref  mathscinet  zmath  isi
    2. S. B. Vakarchuk, “On the best linear approximation methods and the widths of certain classes of analytic functions”, Math. Notes, 65:2 (1999), 153–158  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. M. Sh. Shabozov, O. Sh. Shabozov, “Widths of Some Classes of Analytic Functions in the Hardy Space $H_2$”, Math. Notes, 68:5 (2000), 675–579  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. S. B. Vakarchuk, “Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods”, Math. Notes, 72:5 (2002), 615–619  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Shabozov, MS, “Widths of some classes of analytic functions in the Bergman space”, Doklady Mathematics, 65:2 (2002), 194  isi
    6. Shabozov, MS, “Sharp inequalities between best approximations and moduli of continuity in the Hardy space H-p with 1 <= p <= 2”, Doklady Mathematics, 72:1 (2005), 587  isi
    7. Shabozov, MS, “On the best approximation and exact evaluation of the widths of some classes of functions in the Bergman space B-p, 1 <= p <=infinity”, Doklady Mathematics, 74:2 (2006), 708  crossref  isi
    8. Shabozov, MS, “On the best approximation of some classes of analytic functions in weighted Bergman spaces”, Doklady Mathematics, 75:1 (2007), 97  crossref  isi
    9. S. B. Vakarchuk, V. I. Zabutnaya, “Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$”, Math. Notes, 85:3 (2009), 322–327  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. 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
    11. 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  isi
    12. Vakarchuk S.B., Vakarchuk M.B., “Inequalities of Kolmogorov Type for Analytic Functions of One and Two Complex Variables and their Applications to Approximation Theory”, Ukr. Math. J., 63:12 (2012), 1795–1819  crossref  isi
    13. 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
    14. M. S. Saidusainov, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana”, Chebyshevskii sb., 17:1 (2016), 240–253  mathnet  elib
    15. 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
    16. 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  isi  elib  scopus
    17. M. R. Langarshoev, “O nailuchshem polinomialnom priblizhenii funktsii v vesovom prostranstve Bergmana”, Vladikavk. matem. zhurn., 21:1 (2019), 27–36  mathnet  crossref
    18. M. Sh. Shabozov, M. R. Langarshoev, “O nailuchshikh lineinykh metodakh priblizheniya nekotorykh klassov analiticheskikh v edinichnom kruge funktsii”, Sib. matem. zhurn., 60:6 (2019), 1414–1423  mathnet  crossref
    19. 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
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