Transformation Operator for Jacobi Matrices with Asymptotically Periodic Coefficients |
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Authors: | A Boutet de Monvel |
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Institution: | UFR de Mathématiques, Université Paris 7 Denis Diderot , 2 place Jussieu, 75251, Paris, France |
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Abstract: | We construct the transformation operator for the scattering problem with a periodic background under the assumption that the coefficients of the perturbation have a first finite moment. By means of the Marchenko approach Marchenko, V. (1986) Sturm–Liouville Operators and Applications. Birkhäuser, Basel, Switzerland] we derive an estimate on the kernel of this transformation operator that allow us to study the inverse problem solution in the prescribed class of perturbations. |
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Keywords: | Jacobi operator Scattering problem Asymptotically periodic coefficients Transformation operator 47B36 47A40 |
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