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arXiv · 2610.38603

Matrix orthogonal polynomials related to diffference operators for $L$-orthogonal polynomials

Erik Koelink·Ana Loureiro·Pablo Román
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Abstract

The difference operator $J$ arising from the higher order occurrence for the $L$-orthogonal polynomials is studied using various families of matrix orthogonal polynomials. The matrix orthogonal polynomials determine the polar decomposition of $J$ and its adjoint $J^\ast$ considered as operators on $\ell^2(\mathbb{N})$. The special case of symmetric $J$ leads to the case where the matrix polynomials reduce to diagonal matrix polynomials. The example of the symmetric case with constant coefficients for $L=2$ is discussed in detail.

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Erik Koelink, Ana Loureiro, Pablo Román. 2026-10-28. Matrix orthogonal polynomials related to diffference operators for $L$-orthogonal polynomials. https://arxiv.org/abs/2610.38603

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