Geodesic
Equivalent conditions for representing analytic functions by exponential series
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 91-104 
A. F. Leont'ev. Equivalent conditions for representing analytic functions by exponential series. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 91-104. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a9/
@article{MZM_1976_20_1_a9,
     author = {A. F. Leont'ev},
     title = {Equivalent conditions for representing analytic functions by exponential series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {91--104},
     year = {1976},
     volume = {20},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a9/}
}
TY  - JOUR
AU  - A. F. Leont'ev
TI  - Equivalent conditions for representing analytic functions by exponential series
JO  - Matematičeskie zametki
PY  - 1976
SP  - 91
EP  - 104
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a9/
LA  - ru
ID  - MZM_1976_20_1_a9
ER  - 
%0 Journal Article
%A A. F. Leont'ev
%T Equivalent conditions for representing analytic functions by exponential series
%J Matematičeskie zametki
%D 1976
%P 91-104
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a9/
%G ru
%F MZM_1976_20_1_a9

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

Let $L(\lambda)$ be an entire function of exponential type with simple zeros $\lambda_1, \lambda_2,\dots$; let $\overline D$ be the smallest closed convex set which contains all of the singularities of the function which is associated with $L(\lambda)$ in the sense of Borel. In [1] there are necessary and sufficient conditions on $L(\lambda)$ under which a function $f(z)$ which is analytic in $\overline D$ can be represented in $D$ by a Dirichlet series with exponents $\lambda_1, \lambda_2,\dots$ We obtain new equivalent conditions on $L(\lambda)$.