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Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations. (English) Zbl 1114.35139
Summary: 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.
MSC:
35P25 Scattering theory for PDEs
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35L05 Wave equation
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
47A40 Scattering theory of linear operators
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
81U40 Inverse scattering problems in quantum theory
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