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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Inverse scattering problem for two-dimensional Schrödinger operator

V. Serov / L. Päivärinta

Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Oulu, Finland. E-mail:

Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Helsinki, Finland. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 3, Pages 295–305, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406777340946,

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This work deals with the inverse scattering problem for two-dimensional Schrödinger operator. The following problem is studied: To estimate more accurately first nonlinear term from the Born series which corresponds to the scattering data with all energies and all angles in the scattering amplitude. This estimate allows us to conclude that the singularities and the jumps of the unknown potential can be obtained exactly by the Born approximation. Especially, for the potentials from L p-spaces the approximation agrees with the true potential up to the continuous function.

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