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

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.

29 pages

References in corpus (3)

• Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics
• Scattering Theory for Jacobi Operators with Quasi-Periodic Background
• Marchenko-Ostrovski mappings for periodic Jacobi matrices

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