An inverse spectral theory for finite CMVmatrices

Leonid Golinskii; Mikhail Kudryavtsev

doi:10.3934/ipi.2010.4.93

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2010, Volume 4, Issue 1: 93-110. Doi: 10.3934/ipi.2010.4.93

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An inverse spectral theory for finite CMV matrices

Leonid Golinskii^1, and
Mikhail Kudryavtsev^1,

1.
Institute for Low Temperature Physics and Engineering, 47 Lenin ave., Kharkov, 61103

Received: November 30, 2008

Revised: September 30, 2009

Published: January 2010

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Abstract

For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of reconstructing the matrix by two spectra of CMV operators with different "boundary condition'', and the problem of reconstructing a CMV matrix by its spectrum and the spectrum of the CMV matrix obtained from it by unitary truncation.

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Mathematics Subject Classification: Primary: 15A29; Secondary: 42C05, 15A57.

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