Generalized backscattering and the Lax-Phillips transform
| dc.creator | Melrose, Richard | |
| dc.creator | Uhlmann, Gunther | |
| dc.date | 2007-12-27 | |
| dc.date | 2008-01-03 | |
| dc.date.accessioned | 2026-07-07T08:51:50Z | |
| dc.date.available | 2026-07-07T08:51:50Z | |
| dc.description | Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle $ω=Sθ$ in terms of the incoming angle with $S$ orthogonal and $\Id-S$ invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the modified backscattering map is a local isomorphism near elements of a generic set of potentials. | |
| dc.description | Minor changes, typos corrected, references added | |
| dc.identifier | https://arxiv.org/abs/0712.4236 | |
| dc.identifier | http://arxiv.org/abs/0712.4236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145077 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Generalized backscattering and the Lax-Phillips transform | |
| dc.type | text |