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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.
[1] Khôi, L. H.: Holomorphic Dirichlet series in the half plane. Vietnam J. Math. 26 (1998), 259-271. MR 1684343 | Zbl 0935.30002
[2] Mandelbrojt, S.: Dirichlet series. Rice Inst. Pamphlet 31 159-272 (1944). MR 0012163 | Zbl 0063.03767
[3] Srivastava, B. L.: A Study of Spaces of Certain Classes of Vector Valued Dirichlet Series. Thesis. Indian Institute of Technology Kanpur (1983).
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