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

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

2010-04-15

arxiv.org/abs/1004.2664v5

Inverse Problems 27 (2011)115003

Mathematics

Spectral Theory

29 pages

Scientific paper

10.1088/0266-5611/27/11/115003

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 $S(\l)-1,$ where $S(\l)$ is the scattering matrix.

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