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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

Characterizations of uniform hyperbolicity and spectra of CMV matrices

Pages: 1009 - 1023, Volume 9, Issue 4, August 2016      doi:10.3934/dcdss.2016039

 
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David Damanik - Department of Mathematics, Rice University, Houston, TX 77005, United States (email)
Jake Fillman - Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, United States (email)
Milivoje Lukic - Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada (email)
William Yessen - Department of Mathematics, Rice University, Houston, TX 77005, United States (email)

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.

Keywords:  Linear cocycles, uniform hyperbolicity, CMV matrices, generalized eigenfunctions, orthogonal polynomials.
Mathematics Subject Classification:  Primary: 37D20, 42C05; Secondary: 37A20.

Received: September 2014;      Revised: July 2015;      Available Online: August 2016.

 References