Geodesic
Scattering theory for Jacobi operators with general step-like quasiperiodic background
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 1, pp. 33-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop direct and inverse scattering theory for Jacobi operators with step-like coeffscients which are asymptotically close to different finite-gap quasiperiodic coefficients on different sides. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite first moment. 
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I. Egorova; J. Michor; G. Teschl. Scattering theory for Jacobi operators with general step-like quasiperiodic background. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 1, pp. 33-62. http://geodesic.mathdoc.fr/item/JMAG_2008_4_1_a2/

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