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

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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 $\{\lambda_k\}$ ($k\geqslant1$). 
@article{IM2_1973_7_3_a5,
     author = {A. F. Leont'ev},
     title = {On the representation of analytic functions in a~closed convex region by {a~Dirichlet} series},
     journal = {Izvestiya. Mathematics },
     pages = {573--588},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a5/}
}
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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/