Uniform Szego Cocycles Over Strictly Ergodic Subshifts
Spectral Theory
2014-12-30 v1 Classical Analysis and ODEs
Abstract
We consider ergodic families of Verblunsky coefficients generated by minimal aperiodic subshifts. Simon conjectured that the associated probability measures on the unit circle have essential support of zero Lebesgue measure. We prove this for a large class of subshifts, namely those satisfying Boshernitzan's condition. This is accomplished by relating the essential support to uniform convergence properties of the corresponding Szego cocycles.
Keywords
Cite
@article{arxiv.math/0512033,
title = {Uniform Szego Cocycles Over Strictly Ergodic Subshifts},
author = {David Damanik and Daniel Lenz},
journal= {arXiv preprint arXiv:math/0512033},
year = {2014}
}
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6 pages