Get started
Work

Banded totally positive matrices and normality for mixed multiple orthogonal polynomials

Year: 2024
Type: preprint
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.
DOI: 10.48550/arxiv.2404.13965
Language: English
Open Access status: green
Funders: Universidade de Aveiro, Universidade de Coimbra, Ministério da Ciência, Tecnologia e Ensino Superior, Center for Research and Development in Mathematics and Applications, Fundação para a Ciência e a Tecnologia, Agencia Estatal de Investigación
Awards: Centro de Matemática da Universidade de Coimbra, G2120678701, Centro de Investigação e Desenvolvimento em Matemática e Aplicações, G3069120617, G3818084518, G4941397794, G5575456386, G6997658380, Centro de Investigação e Desenvolvimento em Matemática e Aplicações, G8832587989
OpenAlex ID: W4395065461
Cites:
Cited by: 12
Related to: 10