A study on bornological properties of the space of entire functions of several complex variables

Abstract

Spaces of entire functions of several complex variables occupy an important position in view of their vast applications in various branches of mathematics, for instance, the classical analysis, theory of approximation, theory of
topological bases etc. With an idea of correlating entire functions with certain aspects in the theory of basis in locally convex spaces, we have investigated in this paper the bornological aspects of the space $X$ of integral functions of several complex variables. By $Y$ we denote the space of all power series with positive radius of convergence at the origin. We introduce bornologies on $X$
and $Y$ and prove that $Y$ is a convex bornological vector space which is the completion of the convex bornological vector space $X$.