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

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

2005-11-25

arxiv.org/abs/math-ph/0511078v2

Physics

Mathematical Physics

In this slightly revised version we have reworded some of the theorems, and we updated two references

Scientific paper

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{\"o}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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