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arXiv · 1407.8127

Reflectionless CMV matrices and scattering theory

Sherry Chu·Benjamin Landon·Jane Panangaden
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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.

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Sherry Chu, Benjamin Landon, Jane Panangaden. 2014-07-30. Reflectionless CMV matrices and scattering theory. https://doi.org/10.1007/s11005-015-0748-z

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