## Abstract

We give an explicit parametrization of a set of almost periodic CMV matrices whose spectrum (is equal to the absolute continuous spectrum and) is a homogenous set E lying on the unit circle, for instance a Cantor set of positive Lebesgue measure. First to every operator of this set we associate a function from a certain subclass of the Schur functions. Then it is shown that such a function can be represented by reproducing kernels of appropriated Hardy spaces and, consequently, it gives rise to a CMV matrix of the set under consideration. If E is a finite system of arcs our results become basically the results of Geronimo and Johnson.

Original language | English |
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Pages (from-to) | 91-106 |

Number of pages | 16 |

Journal | Journal of Approximation Theory |

Volume | 139 |

Issue number | 1-2 |

DOIs | |

State | Published - Mar 2006 |

Externally published | Yes |

### Bibliographical note

Funding Information:∗Corresponding author. E-mail address: [email protected] (P. Yuditskii). 1 Supported by the Austrian Science Found FWF, project number: P16390-N04. 2Supported by Marie Curie International Fellowship within the 6th European Programme.

### Funding

∗Corresponding author. E-mail address: [email protected] (P. Yuditskii). 1 Supported by the Austrian Science Found FWF, project number: P16390-N04. 2Supported by Marie Curie International Fellowship within the 6th European Programme.

Funders | Funder number |
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Austrian Science Found FWF | P16390-N04 |