The "Action" Variable is not an Invariant for the Uniqueness in the Inverse Scattering Problem

A. Kheifets; P. Yuditskii

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The "Action" Variable is not an Invariant for the Uniqueness in the Inverse Scattering Problem

A. Kheifets·P. Yuditskii

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Abstract

We 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.

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BibTeX RIS

A. Kheifets, P. Yuditskii. 2002-02-13. The "Action" Variable is not an Invariant for the Uniqueness in the Inverse Scattering Problem. https://arxiv.org/abs/math/0202128

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