Almost periodic Verblunsky coefficients and reproducing kernels on Riemann surfaces

F. Peherstorfer; P. Yuditskii

doi:10.1016/j.jat.2005.06.002

Almost periodic Verblunsky coefficients and reproducing kernels on Riemann surfaces

F. Peherstorfer, P. Yuditskii

Johannes Kepler University Linz

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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
Pages (from-to)	91-106
Number of pages	16
Journal	Journal of Approximation Theory
Volume	139
Issue number	1-2
DOIs	https://doi.org/10.1016/j.jat.2005.06.002
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
Austrian Science Found FWF	P16390-N04

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10.1016/j.jat.2005.06.002

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Almost periodic Verblunsky coefficients and reproducing kernels on Riemann surfaces

Abstract

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