Spectral and scattering theory in perturbed stratified fluids. II. Transmission problems and exterior domains (Q1111866)

[For part I see: J. Math. Pures Appl., IX. Ser. 64, 149-173 (1985; Zbl 0597.76074).] In this paper the author considers the acoustic propagator for transmission problems in exterior domains. The unperturbed problem is a stratified fluid where the sound speed \(c_ 0\) is a function of the depth only. Actually the author considers the case \(c_ 0(y)=c_-\) for \(y<0\); \(c_ 0\) for \(0<y<h\); \(c_+\) for \(h<y\), where \(h>0\), \(0<c_ 0<c_-\leq c_+\), \(y\in {\mathbb{R}}\). This case is particularly interesting since it leads to a multichannel scattering problem. The approach followed by the author allows a unified treatment of a large class of boundary conditions. The fundamental tool is the ``limiting absorption principle'' (Theorems I and II of the paper) which is proved by adapting to the present situation various known results and ideas.