Geodesic
Generalized Backscattering and the Lax-Phillips Transform
Serdica Mathematical Journal, Tome 34 (2008) no. 1, pp. 355-372

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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 w = Sq 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.
Keywords: Radon Transform, Fredholm Family, Holomorphy, Potential Scattering, Inversion 
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Melrose, Richard; Uhlmann, Gunther. Generalized Backscattering and the Lax-Phillips Transform. Serdica Mathematical Journal, Tome 34 (2008) no. 1, pp. 355-372. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_1_a13/