Spectral analysis of an acoustic multistratified perturbed cylinder

We look into the operator of acoustic propagation H := -V . pV,with Dirichlet condition, in a domain R := 0' x IR, 0' being boundedin Rn-'(n > 2). The function p is assumed to be real, greater than astrictly positive constant and belongs to Lm(R). When (-1)3x, + oo itis obtained by short-range and long-range perturbations of the functionspi = p(j) @ l(j = 1,2), where E Lm(R') are real and bounded belowby a strictly positive constant. By using a variant of the conjugateoperator method of Mourre 15], and some ideas of the N-body problem in quantum mechanics, we develop the spectral analysis of operator H

and obtain a limiting absorption principle.