A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle
Gesztesy, Fritz ; Zinchenko, Maxim
arXiv, 0501212 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-01-13
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  Primary 47B36, 34A55, 47A10,  Secondary 34L40 
@article{0501212,
     author = {Gesztesy, Fritz and Zinchenko, Maxim},
     title = {A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit
  Circle},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0501212}
}

Gesztesy, Fritz; Zinchenko, Maxim. A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit
  Circle. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0501212/