On Scattering for CMV Matrices

Details On Scattering for CMV Matrices On Scattering for CMV Matrices

2007-06-20

arxiv.org/abs/0706.2970v1

Mathematics

Spectral Theory

Scientific paper

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.

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