Mixed Multiple Orthogonal Laurent Polynomials on the Unit Circle
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912122498187264 |
|---|---|
| author | Huertas, Edmundo J. Mañas, Manuel |
| author_facet | Huertas, Edmundo J. Mañas, Manuel |
| contents | Mixed orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss--Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relations, and an examination of the degrees of the Laurent polynomials is given. Recurrence relations, expressed in terms of banded matrices, are found. These recurrence relations lay the groundwork for corresponding Christoffel-Darboux kernels and relations, as well as for elucidating the ABC theorem. The paper also develops the theory of diagonal Christoffel and Geronimus perturbations of the matrix of measures. Christoffel formulas are found for both perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed Multiple Orthogonal Laurent Polynomials on the Unit Circle Huertas, Edmundo J. Mañas, Manuel Classical Analysis and ODEs Mathematical Physics Complex Variables 33C45, 33C47, 42C05, 15A23 Mixed orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss--Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relations, and an examination of the degrees of the Laurent polynomials is given. Recurrence relations, expressed in terms of banded matrices, are found. These recurrence relations lay the groundwork for corresponding Christoffel-Darboux kernels and relations, as well as for elucidating the ABC theorem. The paper also develops the theory of diagonal Christoffel and Geronimus perturbations of the matrix of measures. Christoffel formulas are found for both perturbations. |
| title | Mixed Multiple Orthogonal Laurent Polynomials on the Unit Circle |
| topic | Classical Analysis and ODEs Mathematical Physics Complex Variables 33C45, 33C47, 42C05, 15A23 |
| url | https://arxiv.org/abs/2411.10834 |