Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series

It is shown within the framework of nonlocal quantum theory of a one-component scalar field go that for significantly nonlinear interaction Lagrangians $L_I(x)=gU(\varphi(x))$ such that the function $U(\alpha)$ satisfies the condition
$$ \lim_{\alpha\to\pm\infty}\vert U(\alpha)\vert=0, $$
it is possible to choose the noniocal formfactor in such a manner that the $S$-matrix will be finite and unitary in every order of perturbation theory and the perturbation-theory series will converge absolutely in a Euclidean domain.