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arXiv · 1503.04787

Pre-sequences of matrix orthogonal polynomials

Juan Tirao
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Abstract

We introduce the notion of a pre-sequence of matrix orthogonal polynomials to mean a sequence {F_n} of matrix orthogonal functions with respect to a weight function W, satisfying a three term recursion relation and such that det(F_0) is not zero almost everywhere. By now there is a uniform construction of such sequences from irreducible spherical functions of some fixed K-types associated to compact symmetric pairs (G,K) of rank one. Our main result is that {Q_n=F_nF_0^{-1}} is a sequence of matrix orthogonal polynomials with respect to the weight function F_0WF_0*, see Theorem 2.1.

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Juan Tirao. 2015-03-16. Pre-sequences of matrix orthogonal polynomials. https://arxiv.org/abs/1503.04787

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