We prove that in dimension two potential scattering the leading order singularities of the unknown potential are obtained exactly by the Born approximation which corresponds to the scattering data with fixed energy. The proof is based on the new estimates for the Green-Faddeev's function
in L
p(), 1 < p ≤ 2. These estimates allow us to consider the potentials with stronger singularities than in previous publications and with noncompact support.
Editor-in-Chief: Kabanikhin, Sergey I.
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Reconstruction of singularities in two dimensional Schrödinger operator with fixed energy
∗Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, University of Oulu, Finland. E-mail: vserov@cc.oulu.fi
†Department of Computational Mathematics and Cybernetics, Moscow Lomonosov State University, 119992, Moscow, GSP-2, Vorob'evy gory, Russia.
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 12, Issue 4, Pages 413–421, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/1569394042248201,
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