Banded totally positive matrices and normality for mixed multiple orthogonal polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917646858977280 |
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| author | Branquinho, Amílcar Foulquié-Moreno, Ana Mañas, Manuel |
| author_facet | Branquinho, Amílcar Foulquié-Moreno, Ana Mañas, Manuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Banded totally positive matrices and normality for mixed multiple orthogonal polynomials Branquinho, Amílcar Foulquié-Moreno, Ana Mañas, Manuel Classical Analysis and ODEs Mathematical Physics 42C05, 33C45, 33C47, 47B39, 47B36 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. |
| title | Banded totally positive matrices and normality for mixed multiple orthogonal polynomials |
| topic | Classical Analysis and ODEs Mathematical Physics 42C05, 33C45, 33C47, 47B39, 47B36 |
| url | https://arxiv.org/abs/2404.13965 |