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 
@article{UFA_2013_5_3_a8,
     author = {A. S. Krivosheyev and O. A. Krivosheyeva},
     title = {A closedness of set of {Dirichlet} series sums},
     journal = {Ufa mathematical journal},
     pages = {94--117},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a8/}
}
TY  - JOUR
AU  - A. S. Krivosheyev
AU  - O. A. Krivosheyeva
TI  - A closedness of set of Dirichlet series sums
JO  - Ufa mathematical journal
PY  - 2013
SP  - 94
EP  - 117
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a8/
LA  - en
ID  - UFA_2013_5_3_a8
ER  - 
%0 Journal Article
%A A. S. Krivosheyev
%A O. A. Krivosheyeva
%T A closedness of set of Dirichlet series sums
%J Ufa mathematical journal
%D 2013
%P 94-117
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UFA_2013_5_3_a8/
%G en
%F UFA_2013_5_3_a8
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/