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arXiv · 1907.07447

Ladder relations for a class of matrix valued orthogonal polynomials

Alfredo Deaño·Bruno Eijsvoogel·Pablo Román
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Abstract

Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on $\mathbb{R}$, and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form $W(x)=e^{-v(x)}e^{xA} e^{xA^\ast}$ on the real line, where $v$ is a scalar polynomial of even degree with positive leading coefficient and $A$ is a constant matrix.

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Alfredo Deaño, Bruno Eijsvoogel, Pablo Román. 2019-07-17. Ladder relations for a class of matrix valued orthogonal polynomials. https://doi.org/10.1111/sapm.12351

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