Abstract

This paper continues the analysis of the scattering problem for a network of open wave-guides started in Parts I and II. In this part we present explicit, physically motivated radiation conditions that ensure uniqueness of the solution to the scattering problem. These conditions stem from a paper of Vasy (2000) on 3-body Schrödinger operators; we also discuss closely related conditions from a paper of Isozaki (1994). Vasy’s paper also proves the existence of the limiting absorption resolvents, and that the limiting solutions satisfy the radiation conditions. The statements of these results require a calculus of pseudodifferential operators, called the 3-body scattering calculus, which is briefly introduced here. We show that the solutions to the model problems obtained in Part I satisfy these radiation conditions, which makes it possible to prove uniqueness, and therefore existence, for the system of Fredholm integral equations introduced in that paper.

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