Szeg\H{o}'s theorem for matrix orthogonal polynomials
Classical Analysis and ODEs
2012-07-06 v2 Complex Variables
Probability
Rings and Algebras
Abstract
We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szeg\H{o}'s theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager.
Cite
@article{arxiv.1104.4999,
title = {Szeg\H{o}'s theorem for matrix orthogonal polynomials},
author = {Maxim Derevyagin and Olga Holtz and Sergey Khrushchev and Mikhail Tyaglov},
journal= {arXiv preprint arXiv:1104.4999},
year = {2012}
}
Comments
19 pp, typos corrected, introduction expanded