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Coefficient multipliers on spaces of vector-valued entire Dirichlet series

Sharma Akanksha, Girja S. Srivastava

Received February 17, 2016.   First published January 3, 2017.

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).