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arXiv:1104.4999 [math.CA]AbstractReferencesReviewsResources

Szegő's theorem for matrix orthogonal polynomials

Maxim Derevyagin, Olga Holtz, Sergey Khrushchev, Mikhail Tyaglov

Published 2011-04-26, updated 2011-12-21Version 2

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.

Comments: 19 pp, typos corrected, introduction expanded
Journal: Journal of Approximation Theory, 164/9 (2012), 1238-1261
Categories: math.CA, math.CV, math.PR, math.RA
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