On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices
arXiv:math-ph/0511078 · doi:10.1007/s11040-007-9014-7
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.
In this slightly revised version we have reworded some of the theorems, and we updated two references