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Spaces of entire functions represented by vector valued Dirichlet series

Srivastava G. S., Sharma A.

Journal of Mathematics and Applications

2011

Vol. 34

97--107

Spaces of entire functions ƒ represented by vector valued Dirichlet series and having finite order and finite type are considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous functionals is characterized. Proper bases are also characterized in terms of growth parameters.

A study of bornological properties of the space of entire functions represented by multiple Dirichlet series

Abdul-Hussein M. S., Srivastava G. S.

Fasciculi Mathematici

2005

Nr 35

135-150

The space of entire functions represented by Dirichlet series of several complex variables has been studied by S. Dauod [1]. M.D. Patwardhan [6] studied the bornological properties of the space of entire functions represented by power series. In this work we study the bornological aspect of the space Γ of entire functions represented by Dirichlet series of several complex variables. By Γ we denote the space of all analytic functions α (s1, s2) = , having finite abscissa of convergence. We introduce bornologies on&Gamma and Γ and prove that Γ is a convex bornological vector space which is the completion of the convex bornological vector space Γ.