  We develop the techniques of \cite{KS1} and \cite{ES1} in order to derive
dispersive estimates for a matrix Hamiltonian equation defined by linearizing
about a minimal mass soliton solution of a saturated, focussing nonlinear
Schr\"odinger equation {c} i u_t + \Delta u + \beta (|u|^2) u = 0 u(0,x) = u_0
(x), in $\reals^3$. These results have been seen before, though we present a
new approach using scattering theory techniques. In further works, we will
numerically and analytically study the existence of a minimal mass soliton, as
well as the spectral assumptions made in the analysis presented here.
