 0517 Fritz Gesztesy and Maxim Zinchenko
 A BorgType Theorem Associated with Orthogonal Polynomials on the Unit Circle
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Jan 13, 05

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Abstract. We prove a general Borgtype result for reflectionless unitary
CanteroMoralVelazquez (CMV) operators U associated with
orthogonal polynomials on the unit circle. The spectrum of U is
assumed to be a connected arc on the unit circle. This extends
a recent result of Simon in connection with a periodic CMV operator
with spectrum the whole unit circle.
In the course of deriving the Borgtype result we also use
exponential Herglotz representations of Caratheodory functions
to prove an infinite sequence of trace formulas connected with the
CMV operator U.
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