Afrika Matematika

, Volume 29, Issue 3–4, pp 601–614 | Cite as

Growth properties of vector valued Dirichlet series with complex exponents

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Abstract

Several authors have studied the growth properties of Dirichlet series and vector valued Dirichlet series (VVDS). Wen Ping Huang, Ju Hong Ning and Jin Tu have obtained various results by considering Dirichlet series with complex exponents. In this paper we obtainthe characterizations of order and type of vector valued Dirichlet series which generalize some well known results for growth of classical Dirichlet series. Further we have tried to study the growth properties of holomorphic vector valued Dirichlet series with complex exponents.

Keywords

Vector valued Dirichlet series (VVDS) Abscissa of convergence Analytic function Maximum term Order and type Norm Topology 

Mathematics Subject Classification

30B50 30D15 

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsJaypee Institute of Information TechnologyNoidaIndia

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