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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2016, Volume 16, Issue 3, Pages 288–298 (Mi isu647)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation

A. Yu. Trynin

Saratov State University, 83, Astrakhanskaya st., 410012, Saratov, Russia

Abstract: The necessary and sufficient conditions for the uniform convergence of sinc-approximations of functions of bounded variation is obtained. Separately we consider the conditions for the uniform convergence in the interval $ (0,\pi) $ and on the interval $ [0,\pi] $. The impossibility of uniform approximation of arbitrary continuous function of bounded variation on the interval $ [0,\pi]$ is settled. We identify the main error of the sinc-approximations when approaching non-smooth functions in spaces of continuous functions and continuous functions vanishing at the ends of the interval $ [0,\pi] $, equipped with the norm of Chebyshev.

Key words: uniform convergence, sinc-approximations, bounded variation, sinc-approximation.

DOI: https://doi.org/10.18500/1816-9791-2016-16-3-288-298

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UDC: 517.518.85

Citation: A. Yu. Trynin, “Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:3 (2016), 288–298

Citation in format AMSBIB
\Bibitem{Try16}
\by A.~Yu.~Trynin
\paper Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2016
\vol 16
\issue 3
\pages 288--298
\mathnet{http://mi.mathnet.ru/isu647}
\crossref{https://doi.org/10.18500/1816-9791-2016-16-3-288-298}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3557756}
\elib{http://elibrary.ru/item.asp?id=26702018}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. A. Yu. Trynin, “Skhodimost protsessov Lagranzha–Shturma–Liuvillya dlya nepreryvnykh funktsii ogranichennoi variatsii”, Vladikavk. matem. zhurn., 20:4 (2018), 76–91  mathnet  crossref
    3. 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 Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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