On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices

preprint2007arXivOpen access

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{ö}dinger 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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