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arXiv · 2407.20994

On a new equivalence relation for matrix-valued orthogonal polynomials

Ignacio Bono Parisi·Inés Pacharoni·Ignacio Zurrián
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Abstract

In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and how to build such a transformation explicitly. In particular, they allow us to see when and how any given sequence of polynomials is Darboux-related to classic orthogonal polynomials. We also explore the notion of Darboux-irreducibility and study some sequences that are not a Darboux transformation of classical orthogonal polynomials.

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Ignacio Bono Parisi, Inés Pacharoni, Ignacio Zurrián. 2024-07-30. On a new equivalence relation for matrix-valued orthogonal polynomials. https://doi.org/10.1080/10652469.2025.2593327

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