On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices
Mathematical Physics
2020-05-27 v2 math.MP
Spectral Theory
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{\"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.
Cite
@article{arxiv.math-ph/0511078,
title = {On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices},
author = {Luis O. Silva and Ricardo Weder},
journal= {arXiv preprint arXiv:math-ph/0511078},
year = {2020}
}
Comments
In this slightly revised version we have reworded some of the theorems, and we updated two references