Banded totally positive matrices and normality for mixed multiple orthogonal polynomials
Classical Analysis and ODEs
2024-04-23 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2404.13965,
title = {Banded totally positive matrices and normality for mixed multiple orthogonal polynomials},
author = {Amílcar Branquinho and Ana Foulquié-Moreno and Manuel Mañas},
journal= {arXiv preprint arXiv:2404.13965},
year = {2024}
}