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Mat. Sb., 2001, Volume 192, Number 2, Pages 67–86 (Mi msb543)  

This article is cited in 9 scientific papers (total in 9 papers)

On optimal recovery methods in Hardy–Sobolev spaces

K. Yu. Osipenko

Moscow State Aviation Technological University

Abstract: A general approach to the construction of optimal methods of recovery of linear functionals from a known solution of the dual extremal problem is proposed which is based on a certain parametrization of this solution of the dual problem. Using this approach several optimal recovery problems in Hardy–Sobolev classes are successfully solved, including the recovery of functions from information about their Fourier coefficients or about the values of the function at some system of nodes, in the periodic and non-periodic cases.

DOI: https://doi.org/10.4213/sm543

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English version:
Sbornik: Mathematics, 2001, 192:2, 225–244

Bibliographic databases:

UDC: 517.53
MSC: Primary 41A65, 30E10; Secondary 30D50, 33E05
Received: 03.04.2000

Citation: K. Yu. Osipenko, “On optimal recovery methods in Hardy–Sobolev spaces”, Mat. Sb., 192:2 (2001), 67–86; Sb. Math., 192:2 (2001), 225–244

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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. K. Yu. Osipenko, “Best quadrature formulae on Hardy–Sobolev classes”, Izv. Math., 65:5 (2001), 923–939  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. K. Yu. Osipenko, “Optimalnoe vosstanovlenie analiticheskikh funktsii po ikh znacheniyam v ravnomernoi setke na okruzhnosti”, Vladikavk. matem. zhurn., 5:1 (2003), 48–52  mathnet  mathscinet  zmath  elib
    3. Fang Gensun, Li Xuehua, “Comparison theorems of Kolmogorov type and exact values of $n$-widths on Hardy-Sobolev classes”, Math. Comp., 75:253 (2006), 241–258  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. R. R. Akopian, “Optimal recovery of functions analytical in a half-plane”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S1–S11  mathnet  crossref  elib
    5. S. P. Sidorov, “Optimal Recovery of Linear Functionals on Sets of Finite Dimension”, Math. Notes, 84:4 (2008), 561–567  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. 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
    7. 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
    8. S. V. Znamenskii, “Chislennaya otsenka tochnosti interpolyatsii neslozhnykh elementarnykh funktsii”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 69–92  mathnet  crossref
    9. S. V. Znamenskij, “Numerical evaluation of the interpolation accuracy of simple elementary functions”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 93–116  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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