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

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Matematicheskie Zametki, 2002, Volume 72, Issue 5, Pages 665–669
DOI: https://doi.org/10.4213/mzm454 (Mi mzm454)

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

Full-text PDF (178 kB) Citations (19)

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

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.

Received: 12.09.2001

English version:
Mathematical Notes, 2002, Volume 72, Issue 5, Pages 615–619
DOI: https://doi.org/10.1023/A:1021496620022

Bibliographic databases:

UDC: 517.5

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm454

https://doi.org/10.4213/mzm454

https://www.mathnet.ru/eng/mzm/v72/i5/p665

This publication is cited in the following 19 articles:

M. R. Langarshoev, “Nailuchshee priblizhenie analiticheskikh v edinichnom kruge funktsii v vesovom prostranstve Bergmana $\mathscr{B}_{2,\mu}$”, Vestnik rossiiskikh universitetov. Matematika, 29:145 (2024), 65–76
M. R. Langarshoev, A. G. Aidarmamadov, “Nailuchshee priblizhenie analiticheskikh v edinichnom kruge funktsii v vesovom prostranstve Bergmana”, Dalnevost. matem. zhurn., 24:1 (2024), 55–66
M. R. Langarshoev, “O nailuchshem priblizhenii analiticheskikh v kruge funktsii v vesovom prostranstve Bergmana $\mathscr{B}_{2,\mu}$”, Izv. vuzov. Matem., 2024, no. 6, 27–36
M. R. Langarshoev, “On the Best Approximation of Functions Analytic in the Disk in the Weighted Bergman Space ${{\mathcal{B}}_{{2,\mu }}}$”, Russ Math., 68:6 (2024), 21
Mirgand Sh. Shabozov, Muqim S. Saidusajnov, “On widths of some classes of analytic functions in a circle”, Ural Math. J., 10:2 (2024), 121–130
M. Sh. Shabozov, A. A. Shabozova, “O tochnykh znacheniyakh poperechnikov klassov analiticheskikh v kruge funktsii”, Matem. tr., 27:4 (2024), 115–140
M. R. Langarshoev, “Nailuchshee priblizhenie i znacheniya poperechnikov nekotorykh klassov analiticheskikh funktsii v vesovom prostranstve Bergmana $\mathscr{B}_{2,\gamma}$”, Vestnik rossiiskikh universitetov. Matematika, 28:142 (2023), 182–192
M. Sh. Shabozov, Z. Sh. Malakbozov, “Sharp Jackson–Stechkin type inequalities in Hardy space $H_2$ and widths of functional classes”, Ufa Math. J., 15:2 (2023), 74–84
M. Sh. Shabozov, G. A. Yusupov, “O nailuchshem polinomialnom priblizhenii funktsii v prostranstve Khardi $H_{q,R}, (1\le q\le\infty, R\ge 1)$”, Chebyshevskii sb., 24:1 (2023), 182–193
M. Sh. Shabozov, Z. Sh. Malakbozov, “On the best polynomial approximation in Hardy space”, Russian Math. (Iz. VUZ), 66:11 (2022), 97–109
M. R. Langarshoev, “O nailuchshem priblizhenii i znacheniyakh poperechnikov nekotorykh klassov funktsii v vesovom prostranstve Bergmana”, Vestnik rossiiskikh universitetov. Matematika, 27:140 (2022), 339–350
S. B. Vakarchuk, M. B. Vakarchuk, “K -funktsіonali ta ekstremalnі zadachі teorіï aproksimatsіï klasіv analіtichnikh u kruzі funktsіi. I”, Ukr. Mat. Zhurn., 74:4 (2022), 469
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
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
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
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
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
S. B. Vakarchuk, M. Sh. Shabozov, “The widths of classes of analytic functions in a disc”, Sb. Math., 201:8 (2010), 1091–1110
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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