Geodesic
Scattering problem for the one-dimensional discrete Schr\"odinger operator with a decreasing potential
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 35 (2006) no. 1, pp. 83-88

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We consider the one-dimensional discrete Schrödinger operator $H_0+V$ acting on the space $l^2(\mathbb{Z}),$ where $V$ is a decreasing potential. The theorem of existence and uniqueness of the corresponding Lippmann–Schwinger equation is proved. We study the asymptotics behaviour of solutions of this equation. 
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     author = {L. E. Morozova},
     title = {Scattering problem for the one-dimensional discrete {Schr\"odinger} operator with a decreasing potential},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2006_35_1_a4/}
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L. E. Morozova. Scattering problem for the one-dimensional discrete Schr\"odinger operator with a decreasing potential. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 35 (2006) no. 1, pp. 83-88. http://geodesic.mathdoc.fr/item/IIMI_2006_35_1_a4/