Spectral analysis and asymptotic amplitude for a multistratified perturbedlayer

We consider the perturbed operator (H) over cap = -c(2)d del(1/d)del in a m ultistratified layer, where c and d are the celerity and density of the med ium. Results are known (see [6]) if c(2)d is constant, but when it is only L-infinity, there are a lot of ifficulties with de domains of operators. Th anks to an adapted localization of the operators, the spectral analysis is performed (till the asymptotic completude and with different limits in +inf inity and -infinity), without any regularity condition on the coefficients. (C) Academie des Sciences/Elsevier, Paris.