2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63336We give a simple example of non-uniqueness in the inverse scattering for Jacobi matrices: roughly speaking $S$-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 Szegö class; on the other hand the transmission coefficient remains the same. This implies the statement given in the title.Spectral Theorytext