Geodesic
On the representation of analytic functions in a closed convex region by a Dirichlet series
Izvestiya. Mathematics, Tome 7 (1973) no. 3, pp. 573-588 
A. F. Leont'ev. On the representation of analytic functions in a closed convex region by a Dirichlet series. Izvestiya. Mathematics, Tome 7 (1973) no. 3, pp. 573-588. http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a5/
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     title = {On the representation of analytic functions in a~closed convex region by {a~Dirichlet} series},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a closed bounded convex region $\overline D$ we give conditions on $\{\lambda_k\}$ for which any function $f(z)$, analytic in the open region $D$ and continuous together with its first two derivatives on $\overline D$, can be expanded in the closed region $\overline D$ in an absolutely convergent Dirichlet series with exponents $\{\lambda_k\}$ ($k\geqslant1$).

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[2] Leontev A. F., “Predstavlenie funktsii obobschennymi ryadami Dirikhle”, Uspekhi matem. nauk, XXIV:2(146) (1969), 97–164 | MR

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