Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 51-56
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V. N. Spevakov; A. B. Kudryavtsev. Absolute summability of orthogonal series by Euler’s method. Matematičeskie zametki, Tome 21 (1977) no. 1, pp. 51-56. http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a5/
@article{MZM_1977_21_1_a5,
author = {V. N. Spevakov and A. B. Kudryavtsev},
title = {Absolute summability of orthogonal series by {Euler{\textquoteright}s} method},
journal = {Matemati\v{c}eskie zametki},
pages = {51--56},
year = {1977},
volume = {21},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a5/}
}
TY - JOUR
AU - V. N. Spevakov
AU - A. B. Kudryavtsev
TI - Absolute summability of orthogonal series by Euler’s method
JO - Matematičeskie zametki
PY - 1977
SP - 51
EP - 56
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a5/
LA - ru
ID - MZM_1977_21_1_a5
ER -
%0 Journal Article
%A V. N. Spevakov
%A A. B. Kudryavtsev
%T Absolute summability of orthogonal series by Euler’s method
%J Matematičeskie zametki
%D 1977
%P 51-56
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1977_21_1_a5/
%G ru
%F MZM_1977_21_1_a5
We have obtained a sufficient condition for the absolute summability of an orthogonal series by the $(E,1)$ method. We have proved that if the coefficients of the orthogonal series decrease monotonically in absolute value, then the condition we have found is exact. We have shown that for coefficients decreasing not necessarily monotonically the condition given is not exact.
