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Differential properties of matrix orthogonal polynomials

M. J. Cantero·L. Moral·L. Velazquez
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Abstract

In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$ where $A$ and $B$ are matrix polynomials. Several characterizations for these semi-classical functionals are given in terms of the corresponding (left) matrix orthogonal polynomials sequence. They involve a quasi-orthogonality property for their derivatives, a structure relation and a second order differo-differential equation. Finally we illustrate the preceding results with some non-trivial examples.

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M. J. Cantero, L. Moral, L. Velazquez. 2002-05-09. Differential properties of matrix orthogonal polynomials. https://arxiv.org/abs/math/0205094

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