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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 C N (N > 1), or a bounded convex domain in 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.

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We study weighted composition operators acting between Fock spaces. The following results are obtained:(i) Criteria for the boundedness and compactness.(ii) Characterizations of compact differences and essential norm.(iii) Complete descriptions of path connected components and isolated points of the space of composition operators and the space of nonzero weighted composition operators.

Abstract. In this paper we present the following results: a description, via the Laplace transformation of analytic functionals, of the dual to the (DFS)-