  We present a generalized Galitskii approach for the Bethe-Salpeter equation
for the two-particle vertex function of a Fermi system with resonant
interaction by accounting for the resonant state in the scattering potential
and utilizing the universal form of the resonant scattering amplitude. The
procedure can be carried out both for the normal as well as for the condensate
state. In both cases, the vertex function in the vicinity of the resonance is
shown to formally coincide with that obtained for a weakly attractive Fermi
gas. Thus we justify the popular calculational framework in which results for
the weakly attractive Fermi gas are formally extrapolated into the domain of
strong coupling, and further to the repulsive side of the resonance, where
molecular states are formed.
