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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 11, Pages 74–85 (Mi ivm7152)  

This article is cited in 8 scientific papers (total in 8 papers)

The divergence of Lagrange interpolation processes in eigenfunctions of the Sturm–Liouville problem

A. Yu. Trynin

Chair of Mathematical Physics and Computing Mathematics, Saratov State University, Saratov, Russia

Abstract: In this paper we construct the example of a continuous function, for which the Lagrange–Sturm–Liouville process diverges almost everywhere.

Keywords: sampling theorem, interpolation, uniform convergence, sinc approximation.

Full text: PDF file (244 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:11, 66–76

Bibliographic databases:

UDC: 517.518
Received: 25.02.2009

Citation: A. Yu. Trynin, “The divergence of Lagrange interpolation processes in eigenfunctions of the Sturm–Liouville problem”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 11, 74–85; Russian Math. (Iz. VUZ), 54:11 (2010), 66–76

Citation in format AMSBIB
\Bibitem{Try10}
\by A.~Yu.~Trynin
\paper The divergence of Lagrange interpolation processes in eigenfunctions of the Sturm--Liouville problem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 11
\pages 74--85
\mathnet{http://mi.mathnet.ru/ivm7152}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2814566}
\elib{http://elibrary.ru/item.asp?id=14865179}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 11
\pages 66--76
\crossref{https://doi.org/10.3103/S1066369X10110071}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649578550}


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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. A. Yu. Trynin, “On necessary and sufficient conditions for convergence of sinc-approximations”, St. Petersburg Math. J., 27:5 (2016), 825–840  mathnet  crossref  mathscinet  isi  elib
    2. A. Yu. Trynin, “On some properties of sinc approximations of continuous functions on the interval”, Ufa Math. J., 7:4 (2015), 111–126  mathnet  crossref  isi  elib
    3. A. Yu. Trynin, “Approximation of continuous on a segment functions with the help of linear combinations of sincs”, Russian Math. (Iz. VUZ), 60:3 (2016), 63–71  mathnet  crossref  isi
    4. A. Yu. Trynin, “Neobkhodimye i dostatochnye usloviya ravnomernoi na otrezke sink-approksimatsii funktsii ogranichennoi variatsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:3 (2016), 288–298  mathnet  crossref  mathscinet  elib
    5. A. Yu. Trynin, “A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation”, Russian Math. (Iz. VUZ), 62:8 (2018), 51–63  mathnet  crossref  isi
    6. A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108  mathnet  crossref  isi
    7. A. Yu. Trynin, “Skhodimost protsessov Lagranzha–Shturma–Liuvillya dlya nepreryvnykh funktsii ogranichennoi variatsii”, Vladikavk. matem. zhurn., 20:4 (2018), 76–91  mathnet  crossref
    8. A. Yu. Trynin, “Sufficient condition for convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of continuity”, Comput. Math. Math. Phys., 58:11 (2018), 1716–1727  mathnet  crossref  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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