Resumen de A Borg-type theorem associated with orthogonal polynomials on the unit circle

Fritz Gesztesy, Maxim Zinchenko

• We prove a general Borg-type result for reflectionless unitary 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 $U$.