Spectral Analysis of the Acoustic Propagator in a Multistratified Domain

The aim of this paper is to study the acoustic propagator H in a perturbed multistratified domain V with the conjugate operator method. H denotes the self-adjoint operator y=c x.= in L2 V.with a Dirichlet condition at the boundary ­V. Here c denotes the propagation velocity depending on the nature of the stratification of V. We shall give some spectral properties of H and we establish the limiting absorption principle in an optimal scale of Besov spaces.