Construction of a unitary analytic scattering amplitude: (IV). Many two-body channels

We extend previous results concerning the existence of unitary amplitudes that correspond to a given differential cross section to the many-channel case. We use cos θ analyticity and show that all of the one-channel results may be adapted to the more general problem. A new constraint, the commutavity of the dispersive and absorptive parts, is shown to be automatic in all but exceptional singular cases.