The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.
On définit la matrice de diffusion dans un milieu stratifié perturbé. Pour une classe de perturbations, on démontre que la partie principale est un opérateur intégral de Fourier sur la sphère à l'infini. On développe un principe d'absorption limite raffiné. Dans de nombreux cas, le symbole de la matrice de diffusion détermine le comportement asymptotique des perturbations.
Keywords: stratified media, scattering matrix, inverse problems, limiting absorption principle
Mot clés : milieu stratifié, matrice de diffusion, problèmes d'inversion, principe d'absorption limite
@article{AIF_2003__53_2_565_0, author = {Christiansen, Tanya and Joshi, M. S.}, title = {Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations}, journal = {Annales de l'Institut Fourier}, pages = {565--624}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {2}, year = {2003}, doi = {10.5802/aif.1953}, mrnumber = {1990007}, zbl = {01940705}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1953/} }
TY - JOUR AU - Christiansen, Tanya AU - Joshi, M. S. TI - Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations JO - Annales de l'Institut Fourier PY - 2003 SP - 565 EP - 624 VL - 53 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1953/ DO - 10.5802/aif.1953 LA - en ID - AIF_2003__53_2_565_0 ER -
%0 Journal Article %A Christiansen, Tanya %A Joshi, M. S. %T Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations %J Annales de l'Institut Fourier %D 2003 %P 565-624 %V 53 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1953/ %R 10.5802/aif.1953 %G en %F AIF_2003__53_2_565_0
Christiansen, Tanya; Joshi, M. S. Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations. Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 565-624. doi : 10.5802/aif.1953. http://www.numdam.org/articles/10.5802/aif.1953/
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