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2006

Almost periodic Verblunsky coefficients and reproducing kernels on Riemann surfaces

9 years 1 months ago
Almost periodic Verblunsky coefficients and reproducing kernels on Riemann surfaces
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.
Franz Peherstorfer, P. Yuditskii
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JAT
Authors Franz Peherstorfer, P. Yuditskii
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