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

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dc.creatorGesztesy, Fritz
dc.creatorZinchenko, Maxim
dc.date2005-01-14
dc.date.accessioned2026-07-07T05:16:04Z
dc.date.available2026-07-07T05:16:04Z
dc.descriptionWe 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.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0501212
dc.identifierhttp://arxiv.org/abs/math/0501212
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73850
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subjectPrimary 47B36, 34A55, 47A10; Secondary 34L40
dc.titleA Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle
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