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arXiv · 1104.4999

Szegő's theorem for matrix orthogonal polynomials

Maxim Derevyagin·Olga Holtz·Sergey Khrushchev·Mikhail Tyaglov
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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 Szegő's theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager.

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Maxim Derevyagin, Olga Holtz, Sergey Khrushchev, Mikhail Tyaglov. 2011-12-21. Szegő's theorem for matrix orthogonal polynomials. https://doi.org/10.1016/j.jat.2012.05.003

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