Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 363-370
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S. V. Bochkarev. Absolute convergence of Fourier series with respect to bounded systems. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 363-370. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a1/
@article{MZM_1974_15_3_a1,
author = {S. V. Bochkarev},
title = {Absolute convergence of {Fourier} series with respect to bounded systems},
journal = {Matemati\v{c}eskie zametki},
pages = {363--370},
year = {1974},
volume = {15},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a1/}
}
TY - JOUR
AU - S. V. Bochkarev
TI - Absolute convergence of Fourier series with respect to bounded systems
JO - Matematičeskie zametki
PY - 1974
SP - 363
EP - 370
VL - 15
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a1/
LA - ru
ID - MZM_1974_15_3_a1
ER -
%0 Journal Article
%A S. V. Bochkarev
%T Absolute convergence of Fourier series with respect to bounded systems
%J Matematičeskie zametki
%D 1974
%P 363-370
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a1/
%G ru
%F MZM_1974_15_3_a1
In this paper we prove that for the piecewise-linear unit jump approximation the sum of the moduli of the Fourier coefficients with respect to an arbitrary complete orthonormal system, which is totally bounded, has, when averaged over sections, a lower bound of order $\log N$, where $N^{-1}$ is the approximation step.
