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

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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.
28 pages

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Spectral Theory, Mathematical Physics, Primary 47B36, 34A55, 47A10; Secondary 34L40

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http://salesiana.dossiersoluciones.com/handle/123456789/73850

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501212
 http://arxiv.org/abs/math/0501212

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arXiv