A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle |
| |
Authors: | Gesztesy Fritz; Zinchenko Maxim |
| |
Institution: | Department of Mathematics, University of Missouri–Columbia Columbia, MO 65211, USA fritz{at}math.missouri.edu
Department of Mathematics, University of Missouri–Columbia Columbia, MO 65211, USA maxim{at}math.missouri.edu |
| |
Abstract: | We prove a general Borg-type result for reflectionless unitaryCMV operators U associated with orthogonal polynomials on theunit circle. The spectrum of U is assumed to be a connectedarc on the unit circle. This extends a recent result of Simonin connection with a periodic CMV operator with spectrum thewhole unit circle. In the course of deriving the Borg-type result we also use exponentialHerglotz representations of Caratheodory functions to provean infinite sequence of trace formulas connected with the CMVoperator U. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|