Geodesic
On convergence conditions for Dirichlet series on closed polygons
Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 463-481 
V. K. Dzyadyk. On convergence conditions for Dirichlet series on closed polygons. Sbornik. Mathematics, Tome 24 (1974) no. 4, pp. 463-481. http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/
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     author = {V. K. Dzyadyk},
     title = {On convergence conditions for {Dirichlet} series on closed polygons},
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     volume = {24},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_24_4_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper treats the questions of convergence and summability on a convex polygon $Q$ of the Dirichlet series of a function $f(z)$ which is analytic in $Q$ and continuous on $\overline Q$. Necessary and sufficient conditions for convergence are given for the case of a square; in the general case, if the necessary conditions for convergence are satisfied, it is sufficient that the integral $\int_0^1\frac{\omega(f;t)}t\,dt$ converge. Bibliography: 7 titles.

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

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

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

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

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

[6] A. I. Markushevich, “O bazise v prostranstve analiticheskikh funktsii”, Matem. sb., 17 (59) (1945), 211–252 | Zbl

[7] A. Zigmund, Trigonometricheskie ryady, t. 1, izd-vo «Mir», Moskva, 1965 | MR