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Mat. Zametki, 1972, Volume 12, Issue 4, Pages 465–476 (Mi mz9905)  

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

Optimal interpolation of analytic functions

K. Yu. Osipenko

M. V. Lomonosov Moscow State University

Abstract: We construct an optimal interpolation formula for a particular class of analytic functions, optimization being over a set of interpolation methods which are not necessarily linear. Optimal nodes and the norm of the error are found for the optimal interpolation formula.

Full text: PDF file (1096 kB)

English version:
Mathematical Notes, 1972, 12:4, 712–719

Bibliographic databases:

UDC: 517.5
Received: 14.10.1971

Citation: K. Yu. Osipenko, “Optimal interpolation of analytic functions”, Mat. Zametki, 12:4 (1972), 465–476; Math. Notes, 12:4 (1972), 712–719

Citation in format AMSBIB
\Bibitem{Osi72}
\by K.~Yu.~Osipenko
\paper Optimal interpolation of analytic functions
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 4
\pages 465--476
\mathnet{http://mi.mathnet.ru/mz9905}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=325980}
\zmath{https://zbmath.org/?q=an:0248.30033}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 4
\pages 712--719
\crossref{https://doi.org/10.1007/BF01093679}


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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. B. D. Boyanov, “The optimal recovery of smooth functions”, Math. USSR-Sb., 69:2 (1991), 357–377  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Yu. A. Farkov, “Widths of Hardy classes and Bergman classes on the ball in $\mathbb C^n$”, Russian Math. Surveys, 45:5 (1990), 229–231  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. K. Yu. Osipenko, “Best and optimal recovery methods for classes of harmonic functions”, Math. USSR-Sb., 73:1 (1992), 111–133  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. 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
    8. K. Yu. Osipenko, “Best quadrature formulae on Hardy–Sobolev classes”, Izv. Math., 65:5 (2001), 923–939  mathnet  crossref  crossref  mathscinet  zmath  elib
    9. 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
    10. 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
    11. T. E. Bagramyan, “Optimalnoe vosstanovlenie garmonicheskoi funktsii po netochno zadannym znacheniyam operatora radialnogo integrirovaniya”, Vladikavk. matem. zhurn., 14:1 (2012), 22–36  mathnet
    12. Bagramyan T.E., “Optimalnoe vosstanovlenie funktsii po netochno zadannomu preobrazovaniyu radona na klassakh, zadavaemykh stepenyu operatora laplasa”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2013, no. 1, 19–25  elib
    13. 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
    14. Yu. A. Farkov, “On the best linear approximation of holomorphic functions”, J. Math. Sci., 218:5 (2016), 678–698  mathnet  crossref  mathscinet  zmath
    15. T. È. Bagramyan, “Optimal Recovery of Harmonic Functions in the Ball from Inaccurate Information on the Radon Transform”, Math. Notes, 98:2 (2015), 195–203  mathnet  crossref  crossref  mathscinet  isi  elib
    16. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Exactness and optimality of methods for recovering functions from their spectrum”, Proc. Steklov Inst. Math., 293 (2016), 194–208  mathnet  crossref  crossref  mathscinet  isi  elib
    17. Bagramyan T., “The optimal recovery of a function from an inaccurate information on its k -plane transform”, Inverse Probl., 32:6 (2016), 065004  crossref  mathscinet  zmath  isi  elib  scopus
    18. Bagramyan T., “Optimal Inversion of the Noisy Radon Transform on Classes Defined By a Degree of the Laplace Operator”, J. Korea Soc. Ind. Appl. Math., 21:1 (2017), 29–37  crossref  isi
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