Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices

arxiv: 1409.6259 · v3 · pith:CSRMZVEAnew · submitted 2014-09-22 · 🧮 math.SP · math-ph· math.DS· math.MP

Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices

David Damanik (Rice University) , Jake Fillman (Rice University) , Milivoje Lukic (University of Toronto , Rice University) , William Yessen (Rice University) This is my paper

classification 🧮 math.SP math-phmath.DSmath.MP

keywords hyperbolicitymatricesuniformassociatedcharacterizationscircleclasscocycle

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

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Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices

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