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arXiv · 1501.07876

Commutation Relations for Unitary Operators II

M. A. Astaburuaga·O. Bourget·V. H. Cortés
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Abstract

Let $f$ be a regular non-constant symbol defined on the $d$-dimensional torus ${\mathbb T}^d$ with values on the unit circle. Denote respectively by $κ$ and $L$, its set of critical points and the associated Laurent operator on $l^2({\mathbb Z}^d)$. Let $U$ be a suitable unitary local perturbation of $L$. We show that the operator $U$ has finite point spectrum and no singular continuous component away from the set $f(κ)$. We apply these results and provide a new approach to analyze the spectral properties of GGT matrices with asymptotically constant Verblunsky coefficients. The proofs are based on positive commutator techniques. We also obtain some propagation estimates.

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M. A. Astaburuaga, O. Bourget, V. H. Cortés. 2015-01-30. Commutation Relations for Unitary Operators II. https://arxiv.org/abs/1501.07876

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