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

A. Yu. Trynin

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 288-298.

Résumé

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.

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