Scattering Theory for CMV Matrices: Uniqueness, Helson–Szegő and Strong Szegő Theorems

Autor:	Peter Yuditskii, Alexander Kheifets, Franz Peherstorfer, L. Golinskii
Rok vydání:	2011
Předmět:	Algebra and Number Theory Transformation operator Scattering Operator (physics) Mathematical analysis Mathematics::Classical Analysis and ODEs Mathematics::Spectral Theory Matrix (mathematics) Inverse scattering problem Uniqueness Scattering theory Analysis A determinant Mathematics
Zdroj:	Integral Equations and Operator Theory. 69:479-508
ISSN:	1420-8989 0378-620X
DOI:	10.1007/s00020-010-1859-7
Popis:	We develop a scattering theory for CMV matrices, similar to the Faddeev–Marchenko theory. A necessary and sufficient condition is obtained for the uniqueness of the solution of the inverse scattering problem. We also obtain two sufficient conditions for uniqueness, which are connected with the Helson–Szegő and the strong Szegő theorems. The first condition is given in terms of the boundedness of a transformation operator associated with the CMV matrix. In the second case this operator has a determinant. In both cases we characterize Verblunsky parameters of the CMV matrices, corresponding spectral measures and scattering functions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fadfdd500a497dc1d477d9f17ee553f4 https://doi.org/10.1007/s00020-010-1859-7 Zobrazit plný text záznamu Full text from SpringerLink