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Title: Generalized Backscattering and the Lax-Phillips Transform
Authors: Melrose, Richard
Uhlmann, Gunther
Keywords: Radon Transform
Fredholm Family
Potential Scattering
Issue Date: 2008
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 34, No 1, (2008), 355p-372p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 1

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