On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices
Luis O. Silva, Ricardo Weder
Abstract
We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schr\"odinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions.
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