Théorie spectrale de la propagation des ondes acoustiques dans un milieu stratifié perturbe

Generalized eigenfunctions of layered elastic media and application to diffuse fields

“…These eigenvectors are required to construct the complete modal solutions of the elastic wave equation 15 . Our work generalizes previous results obtained in the case of a homogeneous half-space 11,16 . Before stating the Stone formula, we introduce the resolvent G(λ) of the operator L:…”

“…Once the eigenvectors of the transformed operator have been obtained, those pertaining to the original operator are recovered by application of the inverse operation U † . As shown previously 11,12 , the elastodynamic operator is positive definite and self-adjoint in the Hilbert space with scalar product…”

Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations

“…We warn the reader that the choice of the total space dimension to be rt rather than n+ 1 is in disagreement with [5] [3], [13], [32], [34]. [32].)…”

Recovering Asymptotics at Infinity of Perturbations of Stratified Media

“…[2,4,5,17,19] and references). Below we summarize some of the results of other authors that are most relevant here.…”