Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 619-623
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S. A. Telyakovskii. Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity. Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 619-623. http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a8/
@article{MZM_1970_8_5_a8,
author = {S. A. Telyakovskii},
title = {Quasiconvex uniform-convergence factors for {Fourier} series of functions with a~given modulus of continuity},
journal = {Matemati\v{c}eskie zametki},
pages = {619--623},
year = {1970},
volume = {8},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a8/}
}
TY - JOUR
AU - S. A. Telyakovskii
TI - Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity
JO - Matematičeskie zametki
PY - 1970
SP - 619
EP - 623
VL - 8
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a8/
LA - ru
ID - MZM_1970_8_5_a8
ER -
%0 Journal Article
%A S. A. Telyakovskii
%T Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity
%J Matematičeskie zametki
%D 1970
%P 619-623
%V 8
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a8/
%G ru
%F MZM_1970_8_5_a8
It is proved that a quasiconvex sequencelambda $\{\lambda_\nu\}$ of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuity $\omega(\delta)$ into uniformly convergent series if and only iflambda $\lambda_n\omega(1/n)\log n\to0$. The sufficiency of this condition is already known.
