Geodesic
The inverse scattering problem for a~discrete Sturm-Liouville equation on the line
Sbornik. Mathematics, Tome 202 (2011) no. 7, pp. 1071-1083

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This paper investigates the inverse scattering problem for a discrete Sturm-Liouville equation on the entire line with coefficients that stabilize to zero in one direction. We derive a necessary and a sufficient condition on the scattering data so that the inverse problem is uniquely solvable. Bibliography: 23 titles.
Keywords: the inverse spectral problem, Jacobi operators, scattering problem, Weyl function. 
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     author = {A. Kh. Khanmamedov},
     title = {The inverse scattering problem for a~discrete {Sturm-Liouville} equation on the line},
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A. Kh. Khanmamedov. The inverse scattering problem for a~discrete Sturm-Liouville equation on the line. Sbornik. Mathematics, Tome 202 (2011) no. 7, pp. 1071-1083. http://geodesic.mathdoc.fr/item/SM_2011_202_7_a6/