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August  2007, 1(3): 525-535. doi: 10.3934/ipi.2007.1.525

Recovery of jumps and singularities in the multidimensional Schrodinger operator from limited data

Lassi Päivärinta 1, and  Valery Serov 2,

1. 

Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FI-00014
2. 

Department of Mathematical Sciences, University of Oulu, Finland

Received  January 2007 Published  July 2007

The inverse scattering problem for multidimensional Schrödinger operator is studied. More exactly we prove a new formula for the first nonlinear term to estimate more accurately this term. This estimate allows to conclude that all singularities and jumps of the unknown potential can be recovered from the Born approximation. Especially, we show for the potentials in $L^p$ for certain values of $p$ that the approximation agrees with the true potential up to the continuous function.% Text of abstract
Keywords: Born approximation., Inverse problems, Schrödinger operator.
Mathematics Subject Classification: Primary: 81U40, 35P2.
Citation: Lassi Päivärinta, Valery Serov. Recovery of jumps and singularities in the multidimensional Schrodinger operator from limited data. Inverse Problems and Imaging, 2007, 1 (3) : 525-535. doi: 10.3934/ipi.2007.1.525
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