Integral approximation of the characteristic function of an interval and the Jackson inequality in $C(\mathbb T)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 59-65
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An application of the results about integral approximation of the characteristic function of an interval by the subspace $\tau_{n-1}$ of trigonometric polynomials of order at most $n-1$, which were obtained by the authors
earlier, to investigation of the Jackson inequality between the best uniform approximation of a continuous
periodic function by the subspace $\tau_{n-1}$ and its modulus of continuity of the second order is presented.
A respective method of uniform approximation of continuous periodic functions by trigonometric polynomials is
constructed.
Keywords:
integral approximation of a function by polynomials, the Jackson inequality.
@article{TIMM_2009_15_1_a4,
author = {A. G. Babenko and Yu. V. Kryakin},
title = {Integral approximation of the characteristic function of an interval and the {Jackson} inequality in $C(\mathbb T)$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {59--65},
publisher = {mathdoc},
volume = {15},
number = {1},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a4/}
}
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%0 Journal Article %A A. G. Babenko %A Yu. V. Kryakin %T Integral approximation of the characteristic function of an interval and the Jackson inequality in $C(\mathbb T)$ %J Trudy Instituta matematiki i mehaniki %D 2009 %P 59-65 %V 15 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a4/ %G ru %F TIMM_2009_15_1_a4
A. G. Babenko; Yu. V. Kryakin. Integral approximation of the characteristic function of an interval and the Jackson inequality in $C(\mathbb T)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a4/