Characterizations of uniform hyperbolicity and spectra of CMV matrices

David Damanik; Jake  Fillman; Milivoje  Lukic; William  Yessen

doi:10.3934/dcdss.2016039

Article Contents

2016, Volume 9, Issue 4: 1009-1023. Doi: 10.3934/dcdss.2016039

This issue Previous Article On integral separation of bounded linear random differential equations Next Article Multiple homoclinic solutions for a one-dimensional Schrödinger equation

Characterizations of uniform hyperbolicity and spectra of CMV matrices

1.
Department of Mathematics, Rice University, Houston, TX 77005
2.
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061
3.
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4

Received: August 31, 2014

Revised: June 30, 2015

Published: July 2016

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Abstract

We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of GL$(2,\mathbb{C})$ cocycles and establish a Johnson-type theorem for extended CMV matrices, relating the spectrum to the set of points on the unit circle for which the associated Szegő cocycle is not uniformly hyperbolic.

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Mathematics Subject Classification: Primary: 37D20, 42C05; Secondary: 37A20.

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