Sharma Akanksha, Girja S. Srivastava, Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector-62, Noida-201307, Uttar Pradesh, India, e-mail:akanksha0001@gmail.com,gs91490@gmail.com

**Abstract:** 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.

**Keywords:** vector-valued Dirichlet series; analytic function; entire function; dual space; norm

**Classification (MSC 2010):** 30B50, 30D15, 46E40

**DOI:** 10.21136/MB.2017.0026-16

**Full text** available as PDF.

**References:**

[1] *L. H. Khôi*: Holomorphic Dirichlet series in the half plane. Vietnam J. Math. 26 (1998), 259-271. MR 1684343 | Zbl 0935.30002

[2] *S. Mandelbrojt*: Dirichlet series. Rice Inst. Pamphlet 31 159-272 (1944). MR 0012163 | Zbl 0063.03767

[3] *B. L. Srivastava*: A Study of Spaces of Certain Classes of Vector Valued Dirichlet Series. Thesis. Indian Institute of Technology Kanpur (1983).

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