Pre-dual of the Function Algebra A −∞(D) and Representation of Functions in Dirichlet Series

Abstract

In this paper we describe, via the Laplace transformation of analytic functionals, a pre-dual to the function algebra A −∞(D) (D being either a bounded C 2-smooth convex domain in $${\mathbb{C}^N (N > 1)}$$ , or a bounded convex domain in $${\mathbb{C}}$$ ) as a space of entire functions with certain growth. A possibility of representation of functions from the pre-dual space in a form of Dirichlet series with frequencies from D, is also studied.