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Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients | | Maxim Zinchenko
; | | Date: |
4 Aug 2008 | | Abstract: | We prove a general Borg-type inverse spectral result for a reflectionless
unitary CMV operator (CMV for Cantero, Moral, and Vel’azquez) 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. | | Source: | arXiv, 0808.0382 | | Services: | Forum | Review | PDF | Favorites | |
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