Szegő's theorem for matrix orthogonal polynomials

Details Szegő's theorem for matrix orthogonal polynomials Szegő's theorem for matrix orthogonal polynomials

2011-04-26

arxiv.org/abs/1104.4999v2

Mathematics

Classical Analysis and ODEs

19 pp, typos corrected, introduction expanded

Scientific paper

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.

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