Matematičeskie zametki, Tome 79 (2006) no. 6, pp. 870-878
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V. S. Kolesnikov. On the boundedness below of trigonometric polynomials of best approximation. Matematičeskie zametki, Tome 79 (2006) no. 6, pp. 870-878. http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a4/
@article{MZM_2006_79_6_a4,
author = {V. S. Kolesnikov},
title = {On the boundedness below of trigonometric polynomials of best approximation},
journal = {Matemati\v{c}eskie zametki},
pages = {870--878},
year = {2006},
volume = {79},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a4/}
}
TY - JOUR
AU - V. S. Kolesnikov
TI - On the boundedness below of trigonometric polynomials of best approximation
JO - Matematičeskie zametki
PY - 2006
SP - 870
EP - 878
VL - 79
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a4/
LA - ru
ID - MZM_2006_79_6_a4
ER -
%0 Journal Article
%A V. S. Kolesnikov
%T On the boundedness below of trigonometric polynomials of best approximation
%J Matematičeskie zametki
%D 2006
%P 870-878
%V 79
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_6_a4/
%G ru
%F MZM_2006_79_6_a4
As A. S. Belov proved, the partial sums of an even $2\pi$-periodic function f expanded in a Fourier series with convex coefficients $\{a_n\}_{n=0}^\infty$, are uniformly bounded below if the conditions $a_n = O(n^{-1})$, $n\to\infty$, are satisfied; moreover, this assertion is no longer valid if the exponent $-1$ in this condition is replaced by a greater one. In this paper, we obtain analogs of these results for trigonometric polynomials of best approximation to the function $f$ in the metric of $L_{2\pi}^1$.
