  A space $G(M, \varPhi)$ of infinitely differentiable functions in ${\mathbb
R}^n$ constructed with a help of a family
$\varPhi=\{\varphi_m\}_{m=1}^{\infty}$ of real-valued functions $\varphi_m
\in~C({\mathbb R}^n)$ and a logarithmically convex sequence $M$ of positive
numbers is considered in the article. In view of conditions on $M$ each
function of $G(M, \varPhi)$ can be extended to an entire function in ${\mathbb
C}^n$. Imposed conditions on $M$ and $\varPhi$ allow to describe the space of
such extensions.
