Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 129-136
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R. I. Ovsepyan; A. A. Talalyan. Convergence of orthogonal series to $+\infty$. Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 129-136. http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a0/
@article{MZM_1970_8_2_a0,
author = {R. I. Ovsepyan and A. A. Talalyan},
title = {Convergence of orthogonal series to $+\infty$},
journal = {Matemati\v{c}eskie zametki},
pages = {129--136},
year = {1970},
volume = {8},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a0/}
}
TY - JOUR
AU - R. I. Ovsepyan
AU - A. A. Talalyan
TI - Convergence of orthogonal series to $+\infty$
JO - Matematičeskie zametki
PY - 1970
SP - 129
EP - 136
VL - 8
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a0/
LA - ru
ID - MZM_1970_8_2_a0
ER -
%0 Journal Article
%A R. I. Ovsepyan
%A A. A. Talalyan
%T Convergence of orthogonal series to $+\infty$
%J Matematičeskie zametki
%D 1970
%P 129-136
%V 8
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a0/
%G ru
%F MZM_1970_8_2_a0
For any sequence $\{b_n\}$ such that $\sum_{n=1}^\infty b_n^2=\infty$, a uniformly bounded system $\{\Phi_n(x)\}$, orthonormal on $[0, 1]$, is constructed such that the series $\sum_{n=1}^\infty b_n\Phi_n(x)$ diverges to $+\infty$ on some set $E\subset[0, 1]$, $0<\mathrm{mes}\, E<1$, for any order of the terms.
