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

• Autores: Fritz Gesztesy, Maxim Zinchenko
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 74, Nº 3, 2006, págs. 757-777
• Idioma: inglés
• DOI: 10.1112/s0024610706023167
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• Resumen

  • 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 $U$.