Higher order scattering on asymptotically Euclidean manifolds

Authors
Christiansen, TJ Joshi, MS
Citation
Tj. Christiansen et Ms. Joshi, Higher order scattering on asymptotically Euclidean manifolds, CAN J MATH, 52(5), 2000, pp. 897-919
Citations number
18
Categorie Soggetti
Mathematics
Journal title
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN journal
0008414X → ACNP
Volume
52
Issue
5
Year of publication
2000
Pages
897 - 919
Database
ISI
SICI code
0008-414X(200010)52:5<897:HOSOAE>2.0.ZU;2-8
Abstract
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 R-n the asymptot ics of certain short-range perturbations of Delta(k) can be recovered from the scattering matrix at a finite number of energies.