Geodesic
Trigonometric series with monotone coefficients
Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 77-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{a_n\}$ be a monotonically decreasing sequence. Then each sequence $\{b_n\}$ such that $b_n\downarrow0$, $b_n\le a_n$, $n=1,2,\dots$, is a sequence of Fourier-Lebesgue coefficients with respect to the system $\{\cos nx\}$ if and only if the sequence $\sum_{n=1}^\infty\frac{a_n}n$ converges. 
@article{MZM_1977_22_1_a8,
     author = {L. A. Balashov},
     title = {Trigonometric series with monotone coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {77--83},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a8/}
}
TY  - JOUR
AU  - L. A. Balashov
TI  - Trigonometric series with monotone coefficients
JO  - Matematičeskie zametki
PY  - 1977
SP  - 77
EP  - 83
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a8/
LA  - ru
ID  - MZM_1977_22_1_a8
ER  - 
%0 Journal Article
%A L. A. Balashov
%T Trigonometric series with monotone coefficients
%J Matematičeskie zametki
%D 1977
%P 77-83
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a8/
%G ru
%F MZM_1977_22_1_a8
L. A. Balashov. Trigonometric series with monotone coefficients. Matematičeskie zametki, Tome 22 (1977) no. 1, pp. 77-83. http://geodesic.mathdoc.fr/item/MZM_1977_22_1_a8/