Abstract
The Jacobi operator (Jf) n = a n−1 f n−1 +a n f n+1 + b n f n on ℤ with real finitely supported sequences (a n − 1) n∈ℤ and (b n ) n∈ℤ is considered. The inverse problem for two mappings (including their characterization): (a n , b n , n ∈ ℤ) → {the zeros of the reflection coefficient} and (a n , b n , n ∈ ℤ) → {the eigenvalues and the resonances} is solved. All Jacobi operators with the same eigenvalues and resonances are also described.
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Korotyaev, E.L. Inverse resonance scattering for Jacobi operators. Russ. J. Math. Phys. 18, 427–439 (2011). https://doi.org/10.1134/S1061920811040054
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DOI: https://doi.org/10.1134/S1061920811040054