  The transition operator T for the scattering of a particle from N potentials
V_j can be expanded into a series featuring the transition operators t_j
associated with the individual potentials. For V_j(x) both absolutely and
square integrable in x, we show, using an analytic continuation argument, that
if T is on-shell, i.e. in < k|T(sigma^{2}+ i0)|k' >, |k|=|k'|=\sigma, then each
t_j is also on-shell.
