Geodesic
Cauchy--Hadamard theorem for exponential series
Ufa mathematical journal, Tome 6 (2014) no. 1, pp. 71-79

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In this paper we study the connection between the growth of coefficients of an exponentials series with its convergence domain in finite-dimensional real and complex spaces. Among the first results of the subject is the well-known Cauchy–Hadamard formula. We obtain exact conditions on the exponentials and a convex region in which there is a generalization of the Cauchy–Hadamard theorem. To the sequence of coefficients of exponential series we associate a space of sequences forming a commutative ring with unit. The study of the properties of this ring allows us to obtain the results on solvability of non-homogeneous systems of convolution equations.
Keywords: series of exponentials
Mots-clés : convex domains, Cauchy–Hadamard formula. 
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     title = {Cauchy--Hadamard theorem for exponential series},
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S. G. Merzlyakov. Cauchy--Hadamard theorem for exponential series. Ufa mathematical journal, Tome 6 (2014) no. 1, pp. 71-79. http://geodesic.mathdoc.fr/item/UFA_2014_6_1_a6/