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cmv matrix

Mathematical Modelling of Natural Phenomena (1)

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CMV Matrices with Super Exponentially Decaying VerblunskyCoefficients
M. Zinchenko
Journal:

Mathematical Modelling of Natural Phenomena / Volume 9 / Issue 5 / 2014

Published online by Cambridge University Press:

17 July 2014, pp. 282-294

Print publication:

2014
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We investigate several equivalent notions of the Jost solution associated with a unitaryCMV matrix and provide a necessary and sufficient conditions for the Jost solution toconsist of entire functions of finite growth order in terms of super exponential decay ofVerblunsky coefficients. We also establish several one-to-one correspondences between CMVmatrices with super-exponentially decaying Verblunsky coefficients and spectral dataassociated with the first component of the Jost solution.