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Published November 2009 | Submitted
Journal Article Open

Right Limits and Reflectionless Measures for CMV Matrices

Abstract

We study CMV matrices by focusing on their right-limit sets. We prove a CMV version of a recent result of Remling dealing with the implications of the existence of absolutely continuous spectrum, and we study some of its consequences. We further demonstrate the usefulness of right limits in the study of weak asymptotic convergence of spectral measures and ratio asymptotics for orthogonal polynomials by extending and refining earlier results of Khrushchev. To demonstrate the analogy with the Jacobi case, we recover corresponding previous results of Simon using the same approach.

Additional Information

© 2009 Springer. Received: 24 November 2008; Accepted: 10 February 2009; Published online: 29 May 2009. We would like to thank Barry Simon for helpful discussions, as well as the referees for their useful comments.

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