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,π) and on the interval [0,π]. The impossibility of uniform approximation of arbitrary continuous function of bounded variation on the interval [0,π] 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,π], equipped with the norm of Chebyshev.
Citation:
A. Yu. Trynin, “Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation”, Izv. Saratov Univ. Math. Mech. Inform., 16:3 (2016), 288–298
\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. 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://mathscinet.ams.org/mathscinet-getitem?mr=3557756}
\elib{https://elibrary.ru/item.asp?id=26702018}
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https://www.mathnet.ru/eng/isu647
https://www.mathnet.ru/eng/isu/v16/i3/p288
This publication is cited in the following 6 articles:
I. V. Podvigin, “Kriterii stepennoi skorosti skhodimosti ergodicheskikh srednikh dlya unitarnykh deistvii grupp $\mathbb{Z}^d$ i $\mathbb{R}^d$”, Algebra i analiz, 36:4 (2024), 148–164
A. Yu. Trynin, “Lagrange–Sturm–Liouville Processes”, J Math Sci, 261:3 (2022), 455
A. Yu. Trynin, “On the uniform approximation of functions of bounded variation by Lagrange interpolation
polynomials with a matrix ${\mathcal L}_n^{(\alpha_n,\beta_n)}$ of Jacobi nodes”, Izv. Math., 84:6 (2020), 1224–1249
A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108
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
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