On the removal of cutoffs in the $S$-matrix

Bogolyubov's $R$-operation is studied for $H_{\operatorname{int}}=\lambda:\varphi^4(x):$, where $\varphi(x)$ is a generalized free field with space-like regularization. It is shown that the coefficient functions of the perturbation series for the $S$-matrix tend to their renormalized values when the cutoffs are removed.