vector-valued Dirichlet series; analytic function; entire function; dual space; norm
The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space $X$ of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some classes of vector-valued Dirichlet series.
 Khôi, L. H.: Holomorphic Dirichlet series in the half plane
. Vietnam J. Math. 26 (1998), 259-271. MR 1684343
| Zbl 0935.30002
 Srivastava, B. L.: A Study of Spaces of Certain Classes of Vector Valued Dirichlet Series. Thesis. Indian Institute of Technology Kanpur (1983).