English

Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices

Spectral Theory 2016-12-15 v3 Mathematical Physics Dynamical Systems math.MP

Abstract

We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of GL(2,C)\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.

Keywords

Cite

@article{arxiv.1409.6259,
  title  = {Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices},
  author = {David Damanik and Jake Fillman and Milivoje Lukic and William Yessen},
  journal= {arXiv preprint arXiv:1409.6259},
  year   = {2016}
}

Comments

15 pages; based on the appendices of arXiv:1404.7065, which were removed in passing from arXiv:1404.7065v1 to arXiv:1404.7065v2, the latter being the version accepted for publication in IMRN