Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients

Li, Long; Damanik, David; Zhou, Qi

doi:10.1090/tran/8696

Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients
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by Long Li, David Damanik and Qi Zhou PDF

Trans. Amer. Math. Soc. 375 (2022), 6093-6125 Request permission

Abstract:

We consider standard and extended CMV matrices with small quasi-periodic Verblunsky coefficients and show that on their essential spectrum, all spectral measures are purely absolutely continuous. This answers a question of Barry Simon from 2005.

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