caa a22 4500 378896474 CHVBK 20180305123507.0 cr unu---uuuuu 161128e20041001xx s 000 0 eng 10.1515/1569394042248201 doi (NATIONALLICENCE)gruyter-10.1515/1569394042248201 Reconstruction of singularities in two dimensional Schrödinger operator with fixed energy [Elektronische Daten] [V. S. Serov, A. D. Chernova] 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. Copyright 2004, Walter de Gruyter Serov V. S. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, University of Oulu, Finland. E-mail: vserov@cc.oulu.fi aut Chernova A. D. Department of Computational Mathematics and Cybernetics, Moscow Lomonosov State University, 119992, Moscow, GSP-2, Vorob'evy gory, Russia. aut Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/4(2004-10-01), 413-421 0928-0219 12:4<413 2004 12 jiip https://doi.org/10.1515/1569394042248201 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569394042248201 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Serov V. S. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, University of Oulu, Finland. E-mail: vserov@cc.oulu.fi aut NATIONALLICENCE 700 1- Chernova A. D. Department of Computational Mathematics and Cybernetics, Moscow Lomonosov State University, 119992, Moscow, GSP-2, Vorob'evy gory, Russia aut NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 12/4(2004-10-01), 413-421 0928-0219 12:4<413 2004 12 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter