Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 317-328
Citer cet article
S. A. Telyakovskii. Concerning a sufficient condition of Sidon for the integrability of trigonometric series. Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 317-328. http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a1/
@article{MZM_1973_14_3_a1,
author = {S. A. Telyakovskii},
title = {Concerning a sufficient condition of {Sidon} for the integrability of trigonometric series},
journal = {Matemati\v{c}eskie zametki},
pages = {317--328},
year = {1973},
volume = {14},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a1/}
}
TY - JOUR
AU - S. A. Telyakovskii
TI - Concerning a sufficient condition of Sidon for the integrability of trigonometric series
JO - Matematičeskie zametki
PY - 1973
SP - 317
EP - 328
VL - 14
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a1/
LA - ru
ID - MZM_1973_14_3_a1
ER -
%0 Journal Article
%A S. A. Telyakovskii
%T Concerning a sufficient condition of Sidon for the integrability of trigonometric series
%J Matematičeskie zametki
%D 1973
%P 317-328
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a1/
%G ru
%F MZM_1973_14_3_a1
We consider problems concerning integrability and convergence in the metric $L$ of trigonometric series, the coefficients $a_k$ of which satisfy the conditions: $a_k\to0$, there exist numbers $A_k$ such that $A_k\downarrow0$, $\sum A_k<\infty$, and $|\Delta a_k|\le A_k$. The integrability of a series in cosines under these conditions is equivalent to a theorem of Sidon.
