CMV matrices with asymptotically constant coefficients. Szegő--Blaschke class, scattering theory (Q1017705)
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| Language | Label | Description | Also known as |
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| English | CMV matrices with asymptotically constant coefficients. Szegő--Blaschke class, scattering theory |
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CMV matrices with asymptotically constant coefficients. Szegő--Blaschke class, scattering theory (English)
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12 May 2009
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In this paper, scattering theory is extended for CMV matrices with asymptotically constant Verblunsky coefficients. It is shown that the class of two-sided CMV matrices of the Szegő--Blaschke class correspond precisely to the class for which the scattering problem can be posed and solved. CMV matrices are represented as multiplication operators in \(L^{2}\)-spaces with respect to specific bases. A~CMV matrix of this type is determined uniquely by the scattering data, and the associated Gelfand--Levitan--Marchenko transformation operators are bounded.
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CMV matrix
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Jacobi matrix
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scattering theory
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\(A_{2}\) condition
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Carleson condition
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Schur functions
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Verblunsky coefficients
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