Limiting amplitude principle for acoustic propagators in perturbed stratified fluids
Koji Kikuchi, Hideo Tamura · Proceedings of the Japan Academy Series A Mathematical Sciences · 1989
Introduction.Recently the spectral problems for acoustic operators L--:--c(x)2z] in perturbed stratified fluids have been studied by several authors ([1], [2], [7], [8]).Under suitable assumptions on the behavior of sound speed c(x) at infinity, non-existence of eigenvalues and the principle of limiting absorption have been proved for the operator L. In the pre- sent note we study the principle of limiting amplitude for L which has not been discussed in detail in the works above.1. Limiting amplitude principle.The precise formulation of the obtained result requires several notations and assumptions.