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Right Limits and Reflectionless Measures for CMV Matrices

Breuer, Jonathan and Ryckman, Eric and Zinchenko, Maxim (2009) Right Limits and Reflectionless Measures for CMV Matrices. Communications in Mathematical Physics, 292 (1). pp. 1-28. ISSN 0010-3616. doi:10.1007/s00220-009-0839-8. https://resolver.caltech.edu/CaltechAUTHORS:20090911-153602983

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00220-009-0839-8DOIArticle
https://rdcu.be/4c7bPublisherFree ReadCube access
https://arxiv.org/abs/0902.1571arXivDiscussion Paper
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.
Issue or Number:1
DOI:10.1007/s00220-009-0839-8
Record Number:CaltechAUTHORS:20090911-153602983
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090911-153602983
Official Citation:Breuer, J., Ryckman, E. & Zinchenko, M. Commun. Math. Phys. (2009) 292: 1. https://doi.org/10.1007/s00220-009-0839-8
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15814
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:23 Sep 2009 19:37
Last Modified:08 Nov 2021 23:22

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