Abstract
The behavior of sums of multidimensional series of exponents near the boundary of the region of absolute convergence is studied.
References
J. Hadamard, “Essai sur l'étude des fonctions données par leur développment de Taylor,”De Math. Pures et Appl.,4, No. 8, 101–186 (1892).
J. F. Ritt, “Note on Dirichlet series with complex exponents,”Ann. Math.,26, 144 (1925).
K. Nandan, “On the maximum terma, maximum moduli of analytic functions represented by Dirichlet series,”Ann. Polon. Math., No. 28, 213–222 (1973).
K. Nandan, “On the lower order of analytic functions represented by Dirichlet series,”Rev. Roum. Math. Pures et Appl, No. 10, 1361–1368 (1976).
V. S. Boichuk, “On the growth of Dirichlet series absolutely convergent in a half plane,” in:Mathematical Works [in Russian], Naukova Dumka, Kiev (1976).
V. P. Gromov, “To the theory of multiple Dirichlet series. II,”Izv. Akad. Nauk. Arm. SSR. Mat., No. 2, 89–103 (1972).
V. Yu. Makarov, “On the growth of the sum of a multiple series of exponents,”Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 84–86 (1990).
V. M. Tikhomirov,Contemporary Problems in Mathematics. Fundamental Studies [in Russian], Vol. 14, Moscow (1987).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 438–442, April, 1994.
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Makarov, V.Y. Characteristics of power growth of a multidimensional series of exponents. Ukr Math J 46, 464–470 (1994). https://doi.org/10.1007/BF01060418
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DOI: https://doi.org/10.1007/BF01060418