The "Action" Variable is not an Invariant for the Uniqueness in the Inverse Scattering Problem
Spectral Theory
2007-05-23 v1
Abstract
We give a simple example of non-uniqueness in the inverse scattering for Jacobi matrices: roughly speaking -matrix is analytic. Then, multiplying a reflection coefficient by an inner function, we repair this matrix in such a way that it does uniquely determine a Jacobi matrix of Szeg\"o class; on the other hand the transmission coefficient remains the same. This implies the statement given in the title.
Cite
@article{arxiv.math/0202128,
title = {The "Action" Variable is not an Invariant for the Uniqueness in the Inverse Scattering Problem},
author = {A. Kheifets and P. Yuditskii},
journal= {arXiv preprint arXiv:math/0202128},
year = {2007}
}