On a Hilbert space of entire functions

Abstract

Abstract. We consider the Hilbert space 2 of entire functions of variables constructed by means of a convex function in C depending on the absolute value of the variable and growing at infinity faster than | | for each > 0. We study the problem on describing the dual space in terms of the Laplace transform of the functionals. Under certain conditions for the weight function , we obtain the description of the Laplace transform of linear continuous functionals on 2 . The proof of the main result is based on using new properties of Young-Fenchel transform and one result on the asymptotics of the multi-dimensional Laplace integral established by R.A. Bashmakov, K.P. Isaev, R.S. Yulmukhametov.