English

On Scattering for CMV Matrices

Spectral Theory 2007-06-21 v1 Functional Analysis

Abstract

Adamjan-Arov (Lax--Phillips) model space is considered as a scattering representation space for a CMV matrix in context of an extended Marchenko--Faddeev scattering theory. That is, there exists a basis in which the multiplication by independent variable is a CMV matrix. This basis as well as Verblunski coefficients are computed explicitly in terms of Nehari interpolation. Asymptotically the Verblynski coefficients go to zero. Moreover, relations between the basis and wandering subspaces are established. Transformation from scattering representation to spectral representation is given.

Keywords

Cite

@article{arxiv.0706.2970,
  title  = {On Scattering for CMV Matrices},
  author = {A. Kheifets and F. Peherstorfer and P. Yuditskii},
  journal= {arXiv preprint arXiv:0706.2970},
  year   = {2007}
}
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