Some considerations on non renormalizable interactions

A particular class of non renormalizable interactions is studied in the infinite cutoff limit. Arguments presented suggest that the theory is finite after the introduction of a finite number of counter terms. The Green functions are not C (infinite) in the coupling constant at the origin. The same results are obtained using three different techniques: infinite resummation of Feynman graphs in perturbation theory, analogies with second order phase transitions, the use of the renormalization group equation to define the theory