Generalized backscattering and the Lax-Phillips transform

Details Generalized backscattering and the Lax-Phillips transform Generalized backscattering and the Lax-Phillips transform

2007-12-27

arxiv.org/abs/0712.4236v2

Mathematics

Analysis of PDEs

Minor changes, typos corrected, references added

Scientific paper

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 $\omega =S\theta$ 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.

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