Generalized backscattering and the Lax-Phillips transform
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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.
Minor changes, typos corrected, references added
Minor changes, typos corrected, references added