Reflectionless CMV matrices and scattering theory
Mathematical Physics
2015-06-22 v1 math.MP
Spectral Theory
Abstract
Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is reflectionless iff the scattering matrix is off-diagonal which in turn provides a short proof of an important result of [Breuer-Ryckman-Simon]. These developments parallel those recently obtained for Jacobi matrices.
Cite
@article{arxiv.1407.8127,
title = {Reflectionless CMV matrices and scattering theory},
author = {Sherry Chu and Benjamin Landon and Jane Panangaden},
journal= {arXiv preprint arXiv:1407.8127},
year = {2015}
}
Comments
14 pages