Geodesic
On conditions for representability of entire functions by certain general series
Izvestiya. Mathematics, Tome 13 (1979) no. 1, pp. 63-72 
A. F. Leont'ev; Yu. N. Frolov. On conditions for representability of entire functions by certain general series. Izvestiya. Mathematics, Tome 13 (1979) no. 1, pp. 63-72. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a3/
@article{IM2_1979_13_1_a3,
     author = {A. F. Leont'ev and Yu. N. Frolov},
     title = {On conditions for representability of entire functions by certain general series},
     journal = {Izvestiya. Mathematics},
     pages = {63--72},
     year = {1979},
     volume = {13},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a3/}
}
TY  - JOUR
AU  - A. F. Leont'ev
AU  - Yu. N. Frolov
TI  - On conditions for representability of entire functions by certain general series
JO  - Izvestiya. Mathematics
PY  - 1979
SP  - 63
EP  - 72
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a3/
LA  - en
ID  - IM2_1979_13_1_a3
ER  - 
%0 Journal Article
%A A. F. Leont'ev
%A Yu. N. Frolov
%T On conditions for representability of entire functions by certain general series
%J Izvestiya. Mathematics
%D 1979
%P 63-72
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a3/
%G en
%F IM2_1979_13_1_a3

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

Let $f(z)$ be an entire function of order $\rho$ and $L(\lambda)$ an entire function of order $\rho_1>\rho$ with simple zeros $\lambda_1,\dots,\lambda_k,\dots$ . A series $\sum_1^\infty\alpha_kf(\lambda_kz)$ is assigned (according to a specific rule) to an arbitrary entire function $F(z)$ of order $\nu\frac{\rho\rho_1}{\rho_1-\rho}$. Necessary and sufficient conditions on $L(\lambda)$ are found under which this series always converges to $F(z)$ in some topology. Bibliography: 5 titles.

[1] Leontev A. F., “O predstavlenii tselykh funktsii nekotorymi obschimi ryadami”, Matem. sb., 71(113):1 (1966), 3–13 | MR

[2] Shevtsov V. I., “O predstavlenii tselykh funktsii ryadami $\displaystyle\sum_{k=1}^\infty \alpha_kf(\lambda_kz)$”, Matem. zametki, 4:5 (1968), 579–588 | Zbl

[3] Leontev A. F., “Ob usloviyakh razlozhimosti analiticheskikh funktsii v ryady Dirikhle”, Izv. AN SSSR. Ser. matem., 36 (1972), 1282–1295 | MR

[4] Leontev A. F., “Ob odnom funktsionalnom uravnenii”, Izv. AN SSSR. Ser. matem., 29 (1965), 725–756 | MR

[5] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966