Coefficient multipliers on spaces of vector-valued entire Dirichlet series. (English) Zbl 1474.30017

Summary: 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.


30B50 Dirichlet series, exponential series and other series in one complex variable
30D15 Special classes of entire functions of one complex variable and growth estimates
46E40 Spaces of vector- and operator-valued functions
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