Geodesic
On the convergence of orthogonal series to $+\infty$
Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 499-508 
R. I. Ovsepyan. On the convergence of orthogonal series to $+\infty$. Matematičeskie zametki, Tome 11 (1972) no. 5, pp. 499-508. http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a3/
@article{MZM_1972_11_5_a3,
     author = {R. I. Ovsepyan},
     title = {On the convergence of orthogonal series to $+\infty$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {499--508},
     year = {1972},
     volume = {11},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a3/}
}
TY  - JOUR
AU  - R. I. Ovsepyan
TI  - On the convergence of orthogonal series to $+\infty$
JO  - Matematičeskie zametki
PY  - 1972
SP  - 499
EP  - 508
VL  - 11
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a3/
LA  - ru
ID  - MZM_1972_11_5_a3
ER  - 
%0 Journal Article
%A R. I. Ovsepyan
%T On the convergence of orthogonal series to $+\infty$
%J Matematičeskie zametki
%D 1972
%P 499-508
%V 11
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1972_11_5_a3/
%G ru
%F MZM_1972_11_5_a3

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

For any sequence of numbers $a_n\downarrow0$, $\sum_{n=1}^\infty a_n^2=\infty$, a uniformly bounded orthonormal system of continuous functions $\varphi_n(x)$ which is complete in $L_2(0,1)$, and a sequence of numbers $b_n$ ($0) are constructed such that $\sum_{n=1}^\infty b_n\varphi_n(x)=\infty$ everywhere on $(0, 1)$.