arXiv Open Access 2010

Scattering theory for CMV matrices: uniqueness, Helson--Szegő and Strong SzegŐ theorems

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

Lihat Sumber

Abstrak

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 the uniqueness, which are connected with the Helson--Szeg\H o and the Strong Szeg\H o theorems. The first condition is given in terms of the boundedness of a transformation operator associated to 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.

Topik & Kata Kunci

math.SP math.CA

Penulis (4)

L. Golinskii

A. Kheifets

F. Peherstorfer

P. Yuditskii

Format Sitasi

APA MLA BibTeX

Golinskii, L., Kheifets, A., Peherstorfer, F., Yuditskii, P. (2010). Scattering theory for CMV matrices: uniqueness, Helson--Szegő and Strong SzegŐ theorems. https://arxiv.org/abs/1008.3284

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2010
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓