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Mat. Sb., 2010, Volume 201, Number 8, Pages 3–22 (Mi msb7505)  

This article is cited in 18 scientific papers (total in 18 papers)

The widths of classes of analytic functions in a disc

S. B. Vakarchuka*, M. Sh. Shabozovb

a Dnepropetrovsk University of Economics and Law
b Institute of Mathematics, Academy of Sciences of Republic of Tajikistan

Abstract: The precise values of several $n$-widths of the classes $W^m_{p,R}(\Psi)$, $1\le p<\infty$, $m\in\mathbb N$, $R\ge1$, in the Banach spaces $\mathscr L_{p,\gamma}$ and $B_{p,\gamma}$ are calculated, where $\gamma$ is a weight. These are classes of analytic functions $f$ in a disc of radius $R$ whose $m$th derivatives $f^{(m)}$ belong to the Hardy space $H_{p,R}$ and whose angular boundary values have averaged moduli of smoothness of second order which are majorized by the fixed function $\Psi$ on the point set $\{\pi/(2k)\}_{k\in\mathbb N}$. For the classes $W^m_{p,R}(\Psi)$ best linear methods of approximation in $\mathscr L_{p,\gamma}$ are developed. Extremal problems of related content are also considered.
Bibliography: 37 titles.

Keywords: weight function, best linear method of approximation, optimal method of function recovery, best method of coding of functions.
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7505

Full text: PDF file (608 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:8, 1091–1110

Bibliographic databases:

UDC: 517.538.5
MSC: Primary 41A46; Secondary 46E15
Received: 25.11.2008 and 19.04.2010

Citation: S. B. Vakarchuk, M. Sh. Shabozov, “The widths of classes of analytic functions in a disc”, Mat. Sb., 201:8 (2010), 3–22; Sb. Math., 201:8 (2010), 1091–1110

Citation in format AMSBIB
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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. Shabozov M.Sh., Kholmamadova Sh.A., “O poperechnikakh nekotorykh klassov analiticheskikh v kruge funktsii”, Izv. Tulskogo gos. un-ta. Estestvennye nauki, 2012, no. 3, 48–59  elib
    2. Aidarmamadov A.G., “Poperechniki klassov analiticheskikh v edinichnom kruge funktsii v vesovom prostranstve Bergmana”, Dokl. Akademii nauk Respubliki Tadzhikistan, 55:7 (2012), 540–544  elib
    3. Zargarov D.D., “O tochnykh znacheniyakh $n$-poperechnikov klassov analiticheskikh v kruge funktsii v prostranstve Khardi”, Dokl. Akademii nauk Respubliki Tadzhikistan. Otdelenie fiziko-matematicheskikh, khimicheskikh, geologicheskikh i tekhnicheskikh nauk, 2012, no. 2(147), 16–21  elib
    4. M. Sh. Shabozov, M. R. Langarshoev, “The best linear methods and values of widths for some classes of analytic functions in the Bergman weight space”, Dokl. Math., 87:3 (2013), 338–341  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. Sh. Shabozov, M. S. Saidusainov, “Znacheniya $n$-poperechnikov i nailuchshie lineinye metody priblizheniya nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana”, Izvestiya Tulskogo gosudarstvennogo universiteta. Estestvennye nauki, 2014, no. 3, 40–57  elib
    6. M. R. Langarshoev, “O nailuchshem priblizhenii i znachenii poperechnikov nekotorykh klassov funktsii v vesovom prostranstve Bergmana”, Izvestiya Tulskogo gosudarstvennogo universiteta. Estestvennye nauki, 2014, no. 2, 76–89  elib
    7. A. G. Aidarmamadov, “O nailuchshem priblizhenii analiticheskikh funktsii v vesovom prostranstve Bergmana”, Doklady Akademii nauk Respubliki Tadzhikistan, 57:3 (2014), 184–191  elib
    8. M. Sh. Shabozov, G. A. Yusupov, “Nailuchshie lineinye metody priblizheniya i poperechniki nekotorykh klassov funktsii v prostranstve Khardi”, Doklady Akademii nauk Respubliki Tadzhikistan, 57:2 (2014), 97–102  elib
    9. Yu. A. Farkov, “On the best linear approximation of holomorphic functions”, J. Math. Sci., 218:5 (2016), 678–698  mathnet  crossref  mathscinet  zmath
    10. 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
    11. 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
    12. 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  scopus
    13. Mukim S. Saidusajnov, “$\mathcal{K}$-functionals and exact values of $n$-widths in the Bergman space”, Ural Math. J., 3:2 (2017), 74–81  mathnet  crossref  mathscinet
    14. M. Sh. Shabozov, M. S. Saidusainov, “Srednekvadratichnoe priblizhenie funktsii kompleksnoi peremennoi ryadami Fure v vesovom prostranstve Bergmana”, Vladikavk. matem. zhurn., 20:1 (2018), 86–97  mathnet  crossref  elib
    15. M. R. Langarshoev, “O nailuchshem polinomialnom priblizhenii funktsii v vesovom prostranstve Bergmana”, Vladikavk. matem. zhurn., 21:1 (2019), 27–36  mathnet  crossref  elib
    16. 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
    17. 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
    18. 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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