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.

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 $\{\lambda_k\}$ ($k\geqslant1$). 
@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/}
}
TY  - JOUR
AU  - A. F. Leont'ev
TI  - On the representation of analytic functions in a~closed convex region by a~Dirichlet series
JO  - Izvestiya. Mathematics 
PY  - 1973
SP  - 573
EP  - 588
VL  - 7
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a5/
LA  - en
ID  - IM2_1973_7_3_a5
ER  - 
%0 Journal Article
%A A. F. Leont'ev
%T On the representation of analytic functions in a~closed convex region by a~Dirichlet series
%J Izvestiya. Mathematics 
%D 1973
%P 573-588
%V 7
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a5/
%G en
%F IM2_1973_7_3_a5
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/

[1] Leontev A. F., “K voprosu o predstavlenii analiticheskikh funktsii ryadami Dirikhle”, Matem. sb., 80(122):1 (1969), 117–156 | MR

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

[3] Gelfond A. O., “O polnote sistem analiticheskikh funktsii”, Matem. sb., 4(46) (1938), 149–156 | Zbl

[4] Leontev A. F., “O predstavlenii funktsii posledovatelnostyami polinomov Dirikhle”, Matem. sb., 70(112):1 (1966), 132–144 | MR