Geodesic
The representation of regular functions by Dirichlet series
Matematičeskie zametki, Tome 21 (1977) no. 5, pp. 641-651 
Yu. I. Mel'nik. The representation of regular functions by Dirichlet series. Matematičeskie zametki, Tome 21 (1977) no. 5, pp. 641-651. http://geodesic.mathdoc.fr/item/MZM_1977_21_5_a6/
@article{MZM_1977_21_5_a6,
     author = {Yu. I. Mel'nik},
     title = {The representation of regular functions by {Dirichlet} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {641--651},
     year = {1977},
     volume = {21},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_5_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that if a system of exponents has the property that any function regular in a closed convex domain $\overline G$ can be represented in an open domain $G$ by a Dirichlet series, then any function regular only in $G$ can be represented in $G$ by a Dirichlet series with the same system of exponents. A study is made of the representation of functions regular in $\overline G$ by Dirichlet series that converge in $\overline G$.