Fritz Gesztesy and Maxim Zinchenko
A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle
(105K, LaTeX)

ABSTRACT.  We prove a general Borg-type result for reflectionless unitary
Cantero-Moral-Velazquez  (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 Borg-type result we also use
exponential Herglotz representations of Caratheodory functions
to prove an infinite sequence of trace formulas connected with the
CMV operator U.