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

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  • Mathematics

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Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations AN N A L E S D E L’INSTI T U T F O U R IE R ANNALES DE L’INSTITUT FOURIER Tanya CHRISTIANSEN &M. S. JOSHI Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations Tome 53, no 2 (2003), p. 565-624. <http://aif.cedram.org/item?id=AIF_2003__53_2_565_0> © Association des Annales de l’institut Fourier, 2003, tous droits réservés. L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute re- production en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement per- sonnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/ 565 SCATTERING ON STRATIFIED MEDIA: THE MICROLOCAL PROPERTIES OF THE SCATTERING MATRIX AND RECOVERING ASYMPTOTICS OF PERTURBATIONS by T. CHRISTIANSEN and M. S. JOSHI Ann. Inst. Fourier, Grenoble 53, 2 (2003), 565-624 1. Introduction. In this paper, we study the structure of the scattering matrix on a perturbed stratified medium. In particular, we show that its main part is a Fourier integral operator. En route to proving this theorem, we develop an improved limiting absorption principle for a large class of perturbations, using techniques from Fourier analysis and microlocal analysis. As an application of our results, we prove that the asymptotics of a perturbation can be recovered from the scattering matrix at one energy. Recall that a stratified medium is a model space in which sound waves propagate with a variable sound

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