Geodesic
Coefficient multipliers on spaces of vector-valued entire Dirichlet series
Mathematica Bohemica, Tome 142 (2017) no. 3, pp. 299-307
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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.
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.
DOI : 10.21136/MB.2017.0026-16
Classification : 30B50, 30D15, 42B35, 46E40
Keywords: vector-valued Dirichlet series; analytic function; entire function; dual space; norm 
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Akanksha, Sharma; Srivastava, Girja S. Coefficient multipliers on spaces of vector-valued entire Dirichlet series. Mathematica Bohemica, Tome 142 (2017) no. 3, pp. 299-307. doi: 10.21136/MB.2017.0026-16

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

[2] Mandelbrojt, S.: Dirichlet series. Rice Inst. Pamphlet 31 159-272 (1944). | MR | JFM

[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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