Geodesic
On the representation of regular functions by Dirichlet series in a closed disk
Sbornik. Mathematics, Tome 26 (1975) no. 4, pp. 449-457 
Yu. I. Mel'nik. On the representation of regular functions by Dirichlet series in a closed disk. Sbornik. Mathematics, Tome 26 (1975) no. 4, pp. 449-457. http://geodesic.mathdoc.fr/item/SM_1975_26_4_a1/
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     title = {On the representation of regular functions by {Dirichlet} series in a~closed disk},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is shown that every function regular in a disk, whose second derivative satisfies a Lipschitz condition of order $\frac12+\alpha$ ($\alpha>0$) on the boundary of the disk, can be expanded as a Dirichlet series which is absolutely and uniformly convergent in the closed disk. Bibliography: 7 titles.

[1] A. F. Leontev, “K voprosu o predstavlenii analiticheskikh funktsii ryadami Dirikhle”, Matem. sb., 80(132) (1969), 117–156 | MR

[2] A. F. Leontev, “O predstavlenii analiticheskikh funktsii v zamknutoi vypukloi oblasti ryadami Dirikhle”, Izv. AN SSSR, seriya matem., 37 (1973), 577–592 | MR

[3] V. K. Dzyadyk, E. K. Krutigolova, “O predstavlenii analiticheskikh funktsii ryadami Dirikhle na granitse oblasti skhodimosti”, Matem. zametki, 14:6 (1973), 769–780 | MR

[4] A. F. Leontev, “Ob usloviyakh razlozhimosti funktsii v ryady Dirikhle”, Izv. AN SSSR, seriya matem., 36:6 (1972), 1282–1295 | MR | Zbl

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

[6] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[7] A. Zigmund, Trigonometricheskie ryady, t. I, Mir, M., 1965 | MR