Matematičeskie zametki, Tome 10 (1971) no. 1, pp. 33-40
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S. A. Telyakovskii. Uniform-convergence factors for Fourier series of functions with a given modulus of continuity. Matematičeskie zametki, Tome 10 (1971) no. 1, pp. 33-40. http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a4/
@article{MZM_1971_10_1_a4,
author = {S. A. Telyakovskii},
title = {Uniform-convergence factors for {Fourier} series of functions with a~given modulus of continuity},
journal = {Matemati\v{c}eskie zametki},
pages = {33--40},
year = {1971},
volume = {10},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a4/}
}
TY - JOUR
AU - S. A. Telyakovskii
TI - Uniform-convergence factors for Fourier series of functions with a given modulus of continuity
JO - Matematičeskie zametki
PY - 1971
SP - 33
EP - 40
VL - 10
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a4/
LA - ru
ID - MZM_1971_10_1_a4
ER -
%0 Journal Article
%A S. A. Telyakovskii
%T Uniform-convergence factors for Fourier series of functions with a given modulus of continuity
%J Matematičeskie zametki
%D 1971
%P 33-40
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a4/
%G ru
%F MZM_1971_10_1_a4
It is proved that a sequence of factors $\{\lambda_\nu\}$, which are Fourier–Stieitjes coefficients, converts the Fourier series of any function whose modulus of continuity does not exceed a given modulus of continuity $\omega(\delta)$ into a uniformly convergent series, if and only if $\omega(1/n)\int_o^{2\pi}\left|\lambda_0/2+\sum_{\nu=1}^n\lambda_\nu\cos\nu t\right|dt=o(1)$. The sufficiency of this condition is known.
