Geodesic
Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 288-298

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ISU_2016_16_3_a5,
     author = {A. Yu. Trynin},
     title = {Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {288--298},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a5/}
}
TY  - JOUR
AU  - A. Yu. Trynin
TI  - Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2016
SP  - 288
EP  - 298
VL  - 16
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a5/
LA  - ru
ID  - ISU_2016_16_3_a5
ER  - 
%0 Journal Article
%A A. Yu. Trynin
%T Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2016
%P 288-298
%V 16
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a5/
%G ru
%F ISU_2016_16_3_a5
A. Yu. Trynin. Necessary and sufficient conditions for the uniform on a segment sinc-approximations functions of bounded variation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 288-298. http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a5/