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arXiv · 2404.13965

Banded totally positive matrices and normality for mixed multiple orthogonal polynomials

Amílcar Branquinho·Ana Foulquié-Moreno·Manuel Mañas
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Abstract

This paper serves as an introduction to banded totally positive matrices, exploring various characterizations and associated properties. A significant result within is the demonstration that the collection of such matrices forms a semigroup, notably including a subset permitting positive bidiagonal factorization. Moreover, the paper applies this concept to investigate step line normality concerning the degrees of associated recursion polynomials. It presents a spectral Favard theorem, ensuring the existence of measures, thereby guaranteeing that these recursion polynomials represent mixed multiple orthogonal polynomials that maintain normality on the step line indices.

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Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas. 2024-04-22. Banded totally positive matrices and normality for mixed multiple orthogonal polynomials. https://arxiv.org/abs/2404.13965

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