Scattering Theory for Jacobi Operators with General Step-Like Quasiperiodic Background

  • I. Egorova B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
  • J. Michor Imperial College, 180 Queen's Gate, London SW7 2BZ, UK
    International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
  • G. Teschl Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria
    International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria

Анотація

We develop direct and inverse scattering theory for Jacobi operators with step-like coefficients 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.

Mathematics Subject Classification: 47B36, 81U40, 34L25, 39A11.

Ключові слова:

inverse scattering, Jacobi operators, quasiperiodic, step-like

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Як цитувати

(1)
I. Egorova, J. Michor, G. Teschl, Scattering Theory for Jacobi Operators with General Step-Like Quasiperiodic Background, Журн. мат. фіз. анал. геом. 4 (2008), 33-62.

Номер

Том 4 № 1 (2008)

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