A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle

Fritz Gesztesy; Maxim Zinchenko

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A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle

Fritz Gesztesy·Maxim Zinchenko

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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.

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BibTeX RIS

Fritz Gesztesy, Maxim Zinchenko. 2005-01-14. A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle. https://arxiv.org/abs/math/0501212

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