  We discuss the structure of the two- and three-body T-matrices, scattering
matrices, and resolvents continued to the unphysical energy sheets. Our
conclusions arise due to the representations that have been found for
analytically continued momentum-space kernels of the T-operators. These
representations are explicitly written only in terms of the physical-sheet
kernels of the T-matrix itself. One of advantages of the representations in the
three-body case is that they show which portions of the physical-sheet
three-body scattering matrix are ``responsible'' for the resonances associated
with a particular unphysical sheet. A resonance appears to be the energy where
the correspondingly truncated scattering matrix (taken on the physical sheet)
has eigenvalue zero. We also mention applications of this approach to some
specific three-body systems, based on the Faddeev differential equations.
