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

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

2010-08-19

arxiv.org/abs/1008.3284v1

Mathematics

Spectral Theory

29 pages, substantially revised version of arXiv:0807.4017v1 [math.SP]

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Scattering theory for CMV matrices: uniqueness, Helson--Szegő and Strong SzegŐ theorems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scattering theory for CMV matrices: uniqueness, Helson--Szegő and Strong SzegŐ theorems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scattering theory for CMV matrices: uniqueness, Helson--Szegő and Strong SzegŐ theorems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135034