E. I. Zubkova, F. S. Rofe-Beketov, “Necessary and sufficient conditions in inverse scattering problem on the axis for the triangular <nobr>$2\times 2$</nobr> matrix potential”, Zh. Mat. Fiz. Anal. Geom., 2009, Volume 5, Number 3,Pages <nobr>296

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Necessary and sufficient conditions in inverse scattering problem on the axis for the triangular $2\times 2$ matrix potential

E. I. Zubkova^a, F. S. Rofe-Beketov^b

^a Ukrainian State Academy of Railway Transport, 7 Feyerbakh Sq., Kharkiv, 61050, Ukraine
^b Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine

Abstract: The characteristic properties of the scattering data for the Schrödinger operator on the axis with a triangular $2\times 2$ matrix potential are obtained. A difference between the necessary and sufficient conditions for solvability of ISP under consideration, contained in the previous works of the authors, is eliminated.

Key words and phrases: scattering on the axis, inverse problem, triangular matrix potential.

MSC: 47A40, 81U40

Received: 01.10.2008

Language: English