Cite this article as:
Trynin A. Y. 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., 2016, vol. 16, iss. 3, pp. 288-298. DOI: https://doi.org/10.18500/1816-9791-2016-16-3-288-298
Necessary and Sufficient Conditions for the Uniform on a Segment Sinc-approximations Functions of Bounded Variation
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.
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