Szeg\H{o}'s theorem for matrix orthogonal polynomials

TL;DR

This paper extends classical theorems in orthogonal polynomials to the matrix case, including a matrix analogue of Szeg\

Contribution

It introduces a matrix version of Szeg\

Findings

Proves a matrix Szeg\

Provides an elementary proof of Helson-Lowdenslager distance formula

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.