The inverse backscattering problem in three dimensions |
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Authors: | G Eskin J Ralston |
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Institution: | (1) Department of Mathematics, University of California, 90024 Los Angeles, CA, USA |
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Abstract: | This article is a study of the mapping from a potentialq(x) onR
3 to the backscattering amplitude associated with the Hamiltonian –+q(x). The backscattering amplitude is the restriction of the scattering amplitudea(, , k), (, , k)S
2×S
2×+, toa(,–, k). We show that in suitable (complex) Banach spaces the map fromq(x) toa(x/|x|, –x/|x|, |x|) is usually a local diffeomorphism. Hence in contrast to the overdetermined problem of recoveringq from the full scattering amplitude the inverse backscattering problem is well posed. |
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Keywords: | |
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