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Mat. Zametki, 1976, Volume 19, Issue 1, Pages 29–40 (Mi mz7720)  

This article is cited in 13 scientific papers (total in 13 papers)

Best approximation of analytic functions from information about their values at a finite number of points

K. Yu. Osipenko

M. V. Lomonosov Moscow State University

Abstract: For a class of bounded and analytic functions defined in a simply connected region we construct the best linear method of approximation with respect to information about the values of the function at some points of the region. We show it is unique. We obtain limiting relations for the lower bound of the norm of the error of the best method on an arbitrary compacta with connected complement where the lower bound is taken with respect to nodes from the region of analyticity.

Full text: PDF file (719 kB)

English version:
Mathematical Notes, 1976, 19:1, 17–23

Bibliographic databases:

UDC: 517.5
Received: 25.02.1974

Citation: K. Yu. Osipenko, “Best approximation of analytic functions from information about their values at a finite number of points”, Mat. Zametki, 19:1 (1976), 29–40; Math. Notes, 19:1 (1976), 17–23

Citation in format AMSBIB
\Bibitem{Osi76}
\by K.~Yu.~Osipenko
\paper Best approximation of analytic functions from information about their values at a~finite number of points
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 1
\pages 29--40
\mathnet{http://mi.mathnet.ru/mz7720}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=454020}
\zmath{https://zbmath.org/?q=an:0328.30031}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 1
\pages 17--23
\crossref{https://doi.org/10.1007/BF01147612}


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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 methods for approximating analytic functions given with an error”, Math. USSR-Sb., 46:3 (1983), 353–374  mathnet  crossref  mathscinet  zmath
    2. K. Yu. Osipenko, “Heins' problem and optimal extrapolation of analytic functions prescribed with an error”, Math. USSR-Sb., 54:2 (1986), 551–559  mathnet  crossref  mathscinet  zmath
    3. K. Yu. Osipenko, “On best and optimal quadrature formulas on classes of bounded analytic functions”, Math. USSR-Izv., 32:1 (1989), 77–97  mathnet  crossref  mathscinet  zmath
    4. K. Yu. Osipenko, “The Carathéodory–Fejér problem and optimal recovery of derivatives in Hardy spaces”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 21–33  mathnet  crossref  mathscinet  zmath  isi
    5. K. Yu. Osipenko, “On optimal recovery methods in Hardy–Sobolev spaces”, Sb. Math., 192:2 (2001), 225–244  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. K. Yu. Osipenko, “Best quadrature formulae on Hardy–Sobolev classes”, Izv. Math., 65:5 (2001), 923–939  mathnet  crossref  crossref  mathscinet  zmath  elib
    7. 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
    8. 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
    9. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. K. Yu. Osipenko, “Optimal recovery of linear operators in non-Euclidean metrics”, Sb. Math., 205:10 (2014), 1442–1472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. M. P. Ovchintsev, “Optimalnoe vosstanovlenie vtorykh proizvodnykh ot analiticheskikh funktsii po ikh znacheniyam v konechnom chisle tochek”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:4 (2017), 76–82  mathnet  crossref
    12. A. V. Arutyunov, K. Yu. Osipenko, “Recovering linear operators and Lagrange function minimality condition”, Siberian Math. J., 59:1 (2018), 11–21  mathnet  crossref  crossref  isi  elib
    13. N. Temirgaliev, A. Zh. Zhubanysheva, “Kompyuternyi (vychislitelnyi) poperechnik v kontekste obschei teorii vosstanovleniya”, Izv. vuzov. Matem., 2019, no. 1, 89–97  mathnet  crossref
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