Bornological spaces of entire functions represented by Dirichlet series having slow growth

Abstract

The study of spaces of entire functions was initiated by V.G.Iyer [6] and the space of entire functions represented by Dirichlet series has been studied by Hussein and Kamthan [4] and others. Patwardhan [9] has succesfully studied bornological properties of the spaces of entire function in terms of the coefficients of Taylor series expansions. In this paper we have used another norm and study the bornological aspects of the space $\Gamma$ of all entire Dirichlet series $\alpha(s)=\sum_{n=1}^\infty a_n\exp(s\lambda_n)$ of order zero.

Keywords

• Representations of entire functions by series and integrals