Mathematica Bohemica, online first, 9 pp.

Coefficient multipliers on spaces of vector-valued entire Dirichlet series

Sharma Akanksha, Girja S. Srivastava

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

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

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.

  [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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