Article
Ufa Mathematical Journal
Volume 5, Number 3, pp. 94-117
A closedness of set of Dirichlet series sum.
Krivosheyev A.S., Krivosheyeva O.A.
DOI:10.13108/2013-5-3-94
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In the work we consider Dirichlet series. We study the problem of closedness for the set of the sums for such series in the space of functions holomorphic in a convex domain of a complex plane with a topology of uniform convergence on compact subsets. We obtain necessary and sufficient conditions under those each function in the closure of a linear span of exponents with positive indices is represented by a Dirichlet series. These conditions can be formulated only in terms of geometric characteristics of an index sequence and of the convex domain.