Higher Order Scattering on Asymptotically Euclidean Manifolds

Christiansen, T. J. ; Joshi, M. S.

Canadian journal of mathematics, Tome 52 (2000) no. 5, pp. 897-919

Résumé

We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time $\pi $ on the boundary. Furthermore, it is shown that on ${{\mathbb{R}}^{n}}$ the asymptotics of certain short-range perturbations of ${{\Delta }^{k}}$ can be recovered from the scattering matrix at a finite number of energies.

Détail

DOI : 10.4153/CJM-2000-038-5

Mots-clés : 58G15, scattering theory, conormal, Lagrangian

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