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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A condition for purely absolutely continuous spectrum for CMV operators using the density of states
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by Jake Fillman and Darren C. Ong PDF
Proc. Amer. Math. Soc. 146 (2018), 571-580 Request permission


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 that the spectral type of such a family is almost surely purely absolutely continuous if and only if the density of states is absolutely continuous and the Lyapunov exponent vanishes almost everywhere with respect to the same. Both of these results are CMV operator analogues of theorems obtained by Kotani for Schrödinger operators.
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Additional Information
  • Jake Fillman
  • Affiliation: Mathematics (MC0123), Virginia Tech, 225 Stanger Street, Blacksburg, Virginia 24061
  • MR Author ID: 1065002
  • Email:
  • Darren C. Ong
  • Affiliation: Department of Mathematics, Xiamen University Malaysia, Jalan Sunsuria, Bandar Sunsuria, 43900 Sepang, Selangor Darul Ehsan, Malaysia
  • MR Author ID: 845285
  • Email:
  • Received by editor(s): December 9, 2016
  • Published electronically: October 30, 2017
  • Communicated by: Michael Hitrik
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 571-580
  • MSC (2010): Primary 47B36
  • DOI:
  • MathSciNet review: 3731692