Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients

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dc.creatorZinchenko, Maxim
dc.date2008-08-04
dc.date.accessioned2026-07-07T10:04:50Z
dc.date.available2026-07-07T10:04:50Z
dc.descriptionWe prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Velázquez) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit circle. This extends a recent result on CMV operators with scalar-valued coefficients. In the course of deriving the Borg-type result we also use exponential Herglotz representations of Caratheodory matrix-valued functions to prove an infinite sequence of trace formulas connected with CMV operators.
dc.identifierhttps://arxiv.org/abs/0808.0382
dc.identifierhttp://arxiv.org/abs/0808.0382
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169822
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject47B36; 34A55; 47A10
dc.titleTrace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients
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