Geodesic
On the system $\{f(\lambda_{j}z)\}$ series
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 637-652 
E. N. Alekseeva. On the system $\{f(\lambda_{j}z)\}$ series. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 3, pp. 637-652. http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a0/
@article{FPM_1997_3_3_a0,
     author = {E. N. Alekseeva},
     title = {On the system $\{f(\lambda_{j}z)\}$ series},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {637--652},
     year = {1997},
     volume = {3},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a0/}
}
TY  - JOUR
AU  - E. N. Alekseeva
TI  - On the system $\{f(\lambda_{j}z)\}$ series
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1997
SP  - 637
EP  - 652
VL  - 3
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a0/
LA  - ru
ID  - FPM_1997_3_3_a0
ER  - 
%0 Journal Article
%A E. N. Alekseeva
%T On the system $\{f(\lambda_{j}z)\}$ series
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1997
%P 637-652
%V 3
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_1997_3_3_a0/
%G ru
%F FPM_1997_3_3_a0

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

The aim of the paper is to search the conditions of the expansion of the functions analytical in a unit circle in a series of the $\sum\limits_{j=1}^{\infty}d_{j}f(\lambda_{j}z)$ kind, where $f(z)$ is the function analytical in a unit circle, $|\lambda_{j}|1$. The proved theorems contain as a special case the well-known results about the expansion of analytical functions in the rational series of the form $\sum\limits_{j=1}^{\infty}\frac{d_{j}}{1-\lambda_{j}z}$.