A study of bornological properties of the space of entire functions represented by multiple Dirichlet series
2005
scientific article
english
- convex bornological vector space
- Dirichlet series
EN 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.
135 - 150
CC BY-NC-ND (attribution - noncommercial - no derivatives)
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