Local properties of nonrenormalizable interactions

The possibility of constructing strictly localizable fields is considered, using generalized S-type spaces as spaces of basis functions. The restrictions imposed on the asymptotic behavior of the amplitudes coincide with the well-known restrictions found by Jaffe. Contrary to previous results, the spatial amplitudes and momenta are regular, and not singular functions, in the case considered. The possibility of formulating spectral conditions is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 76–81, August, 1971.