Growth properties of vector valued Dirichlet series with complex exponents
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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.
KeywordsVector valued Dirichlet series (VVDS) Abscissa of convergence Analytic function Maximum term Order and type Norm Topology
Mathematics Subject Classification30B50 30D15
- 6.Nandan, K: On the maximum term and maximum modulus of analytic functions represented by Dirichlet series. Ann. Polon. Math. XXVIII, 213–222 (1975)Google Scholar
- 8.Srivastava, B.L.: A study of spaces of certain classes of vector valued Dirichlet series, thesis, I.I.T Kanpur (1983)Google Scholar