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arXiv · 1206.4785

Spectral decomposition and matrix-valued orthogonal polynomials

Wolter Groenevelt·Mourad E. H. Ismail·Erik Koelink
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Abstract

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from scalar-valued orthogonal polynomials is presented. Two examples of matrix-valued orthogonal polynomials with explicit orthogonality relations and three-term recurrence relation are presented, which both can be considered as $2\times 2$-matrix-valued analogues of subfamilies of Askey-Wilson polynomials.

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Wolter Groenevelt, Mourad E. H. Ismail, Erik Koelink. 2012-06-21. Spectral decomposition and matrix-valued orthogonal polynomials. https://arxiv.org/abs/1206.4785

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