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Abstract: We consider the periodic Jacobi operator $J$ with finitely supportedperturbations on the half-lattice. We describe all eigenvalues and resonancesof $J$ and give their properties. We solve the inverse resonance problem: weprove that the mapping from finitely supported perturbations to the Jostfunctions is one-to-one and onto, we show how the Jost functions can bereconstructed from the eigenvalues, resonances and the set of zeros of$S\l-1,$ where $S\l$ is the scattering matrix.



Author: Alexei Iantchenko, Evgeny Korotyaev

Source: https://arxiv.org/







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