On a class of Verblunsky parameters that corresponds to Guseinov's class of Jacobi parameters

L. Golinskii; A. Kheifets; F. Peherstorfer; P. Yuditskii

On a class of Verblunsky parameters that corresponds to Guseinov's class of Jacobi parameters

L. Golinskii
, A. Kheifets
, F. Peherstorfer
, P. Yuditskii

NASU - B. Verkin Institute for Low Temperature Physics and Engineering
University of Massachusetts Lowell
Johannes Kepler University Linz

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

Abstract

The direct and inverse Geronimus relations between Verblunsky parameters of measures on the unit circle and Jacobi parameters of their Szego{double acute} transforms have been used to prove that Guseinov's class of Jacobi parameters, is in a canonical correspondence with the followingclass of Verblunsky parameters α_n → 0.

Original language	English
Pages (from-to)	277-290
Number of pages	14
Journal	Journal of Mathematical Physics, Analysis, Geometry
Volume	6
Issue number	3
State	Published - 2010
Externally published	Yes

Keywords

Direct and inverse Geronimus relations
Jacobi matrices
Spectral measure
Szego{double acute} transform
Verblunsky coefficients

Cite this

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abstract = "The direct and inverse Geronimus relations between Verblunsky parameters of measures on the unit circle and Jacobi parameters of their Szego\{double acute\} transforms have been used to prove that Guseinov's class of Jacobi parameters, is in a canonical correspondence with the followingclass of Verblunsky parameters αn → 0.",

keywords = "Direct and inverse Geronimus relations, Jacobi matrices, Spectral measure, Szego\{double acute\} transform, Verblunsky coefficients",

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AU - Golinskii, L.

AU - Kheifets, A.

AU - Peherstorfer, F.

AU - Yuditskii, P.

PY - 2010

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N2 - The direct and inverse Geronimus relations between Verblunsky parameters of measures on the unit circle and Jacobi parameters of their Szego{double acute} transforms have been used to prove that Guseinov's class of Jacobi parameters, is in a canonical correspondence with the followingclass of Verblunsky parameters αn → 0.

AB - The direct and inverse Geronimus relations between Verblunsky parameters of measures on the unit circle and Jacobi parameters of their Szego{double acute} transforms have been used to prove that Guseinov's class of Jacobi parameters, is in a canonical correspondence with the followingclass of Verblunsky parameters αn → 0.

KW - Direct and inverse Geronimus relations

KW - Jacobi matrices

KW - Spectral measure

KW - Szego{double acute} transform

KW - Verblunsky coefficients

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ER -

On a class of Verblunsky parameters that corresponds to Guseinov's class of Jacobi parameters

Abstract

Keywords

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