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Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data

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Abstract

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.

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Authors and Affiliations

  1. Institute for Low Temperature Physics, 47, Lenin ave, 61103, Kharkiv, Ukraine

    Iryna Egorova

  2. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Wien, Austria

    Johanna Michor & Gerald Teschl

  3. International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090, Wien, Austria

    Johanna Michor & Gerald Teschl

Authors
  1. Iryna Egorova
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  2. Johanna Michor
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  3. Gerald Teschl
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Correspondence to Gerald Teschl.

Additional information

Research supported by the Austrian Science Fund (FWF) under Grants No. Y330 and V120.

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Egorova, I., Michor, J. & Teschl, G. Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data. Math Phys Anal Geom 16, 111–136 (2013). https://doi.org/10.1007/s11040-012-9121-y

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  • DOI: https://doi.org/10.1007/s11040-012-9121-y

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