Geodesic
A closedness of set of Dirichlet series sums
Ufa mathematical journal, Tome 5 (2013) no. 3, pp. 94-117

Voir la notice de l'article provenant de la source Math-Net.Ru

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 every function from 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.
Keywords: exponent, Dirichlet series, entire function, invariant subspace.
Mots-clés : convex domain 
A. S. Krivosheyev; O. A. Krivosheyeva. A closedness of set of Dirichlet series sums. Ufa mathematical journal, Tome 5 (2013) no. 3, pp. 94-117. http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a8/
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