# A Note on Reflectionless Jacobi Matrices

@article{Jaksic2013ANO,
title={A Note on Reflectionless Jacobi Matrices},
author={Vojkan Jaksic and Benjamin Landon and Annalisa Panati},
journal={Communications in Mathematical Physics},
year={2013},
volume={332},
pages={827-838}
}
• Published 8 August 2013
• Mathematics
• Communications in Mathematical Physics
The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a characterization in terms of stationary scattering theory (the vanishing of the reflection coefficients) and prove that this characterization is equivalent to the usual ones. We also show that the new characterization is equivalent to the notion of being…
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