  A weighted Hilbert space $F^2_{\varphi}$ of entire functions of $n$ variables
is considered in the paper. The weight function $\varphi$ is a convex function
on ${\mathbb C}^n$ depending on modules of variables and growing at infinity
faster than $a \Vert z \Vert$ for each $a > 0$. The problem of description of
the strong dual of this space in terms of the Laplace transformation of
functionals is studied in the article. Under some additional conditions on
$\varphi$ the space of the Laplace transforms of linear continuous functionals
on $F^2_{\varphi}$ is described. The proof of the main result is based on new
properties of the Young-Fenchel transformation and a result of R.A. Bashmakov,
K.P. Isaev and R.S. Yulmukhametov on asymptotics of multidimensional Laplace
transform.
