Periodic Jacobi operator with finitely supported perturbation on the half-lattice

Alexei Iantchenko; Evgeny Korotyaev

doi:10.1088/0266-5611/27/11/115003

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arXiv · 1004.2664

Periodic Jacobi operator with finitely supported perturbation on the half-lattice

Alexei Iantchenko·Evgeny Korotyaev

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Abstract

We consider the periodic Jacobi operator $J$ with finitely supported perturbations on the half-lattice. We describe all eigenvalues and resonances of $J$ and give their properties. We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the Jost functions is one-to-one and onto, we show how the Jost functions can be reconstructed from the eigenvalues, resonances and the set of zeros of $S(ł)-1,$ where $S(ł)$ is the scattering matrix.

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BibTeX RIS

Alexei Iantchenko, Evgeny Korotyaev. 2011-10-16. Periodic Jacobi operator with finitely supported perturbation on the half-lattice. https://doi.org/10.1088/0266-5611%2F27%2F11%2F115003

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