most citedPurely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks

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math.SP2016

A condition for purely absolutely continuous spectrum for CMV operators using the density of states

Jake Fillman, Darren C. Ong

We prove an averaging formula for the derivative of the absolutely continuous part of the density of states measure for an ergodic family of CMV matrices. As a consequence, we show…

math.SP2016★ 2 cited

Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks

Jake Fillman, Darren C. Ong

We show that a generic element of a space of limit-periodic CMV operators has zero-measure Cantor spectrum. We also prove a Craig--Simon type theorem for the density of states meas…