Resumen de Dual of the function algebra $A^{-\infty }(D)$ and representation of functions in Dirichlet series

Alexander V. Abanin, Le Hai Khoi

• In this paper we present the following results: a description, via the Laplace transformation of analytic functionals, of the dual to the (DFS)-space ( being either a bounded -smooth convex domain in , with , or a bounded convex domain in ) as an (FS)-space of entire functions satisfying a certain growth condition; an explicit construction of a countable sufficient set for ; and a possibility of representating functions from in the form of Dirichlet series.