Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Trynin A. Y. Necessary and Sufficient Conditions for the Uniform on a Segment Sinc-approximations Functions of Bounded Variation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 3, pp. 288-298. DOI: 10.18500/1816-9791-2016-16-3-288-298, EDN: WMIIGX

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.09.2016
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Russian
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Mathematics
UDC: 
517.518.85
DOI: 
10.18500/1816-9791-2016-16-3-288-298
EDN: 
WMIIGX

Necessary and Sufficient Conditions for the Uniform on a Segment Sinc-approximations Functions of Bounded Variation

Autors: 
Trynin Aleksandr Yurievich, Saratov State University
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. 

Key words: 
uniform convergence
sinc-approximations
bounded variation
sinc-approximation
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Received: 
12.04.2016
Accepted: 
28.08.2016
Published: 
30.09.2016
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