Mixed-type multiple orthogonal Laurent polynomials on the unit circle
Mixed-type 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 relation...
| Authors: | ; |
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| Format: | Article |
| Publication date: | 2025 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/68062 |
| Online Access: | http://hdl.handle.net/10017/68062 https://dx.doi.org/10.1016/j.cam.2025.117037 |
| Access Level: | Open access |
| Keyword: | Mixed-type multiple orthogonal Laurent polynomials Unit circle Christoffel-Darboux formulas ABC theorem Recurrence relations Christoffel perturbations Geronimus perturbations Matemáticas Mathematics |
| _version_ | 1878733844622868480 |
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| author | Huertas Cejudo, Edmundo José|||0000-0001-6802-3303 |
| author2 | Mañas Baena, Manuel |
| author2_role | author |
| author_browse | Huertas Cejudo, Edmundo José|||0000-0001-6802-3303 Mañas Baena, Manuel |
| author_facet | Huertas Cejudo, Edmundo José|||0000-0001-6802-3303 Mañas Baena, Manuel |
| author_role | author |
| collection | e_Buah Biblioteca Digital Universidad de Alcalá |
| description | Mixed-type 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_5e1dbd255eae15583e91eefa2ee950a8 |
| institution | Universidad de Alcalá (UAH) |
| instname_str | Universidad de Alcalá (UAH) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ebuah.uah.es:10017/68062 |
| publishDate | 2025 |
| publishDateSort | 2025 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | e_Buah Biblioteca Digital Universidad de Alcalá |
| spelling | Mixed-type multiple orthogonal Laurent polynomials on the unit circle Huertas Cejudo, Edmundo José|||0000-0001-6802-3303 Mañas Baena, Manuel Mixed-type multiple orthogonal Laurent polynomials Unit circle Christoffel-Darboux formulas ABC theorem Recurrence relations Christoffel perturbations Geronimus perturbations Matemáticas Mathematics Mixed-type 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. Agencia Estatal de Investigación Comunidad de Madrid Elsevier http://hdl.handle.net/10017/68062 https://dx.doi.org/10.1016/j.cam.2025.117037 |
| spellingShingle | Mixed-type multiple orthogonal Laurent polynomials on the unit circle Huertas Cejudo, Edmundo José|||0000-0001-6802-3303 Mixed-type multiple orthogonal Laurent polynomials Unit circle Christoffel-Darboux formulas ABC theorem Recurrence relations Christoffel perturbations Geronimus perturbations Matemáticas Mathematics |
| title | Mixed-type multiple orthogonal Laurent polynomials on the unit circle |
| title_full | Mixed-type multiple orthogonal Laurent polynomials on the unit circle |
| title_fullStr | Mixed-type multiple orthogonal Laurent polynomials on the unit circle |
| title_full_unstemmed | Mixed-type multiple orthogonal Laurent polynomials on the unit circle |
| title_short | Mixed-type multiple orthogonal Laurent polynomials on the unit circle |
| title_sort | Mixed-type multiple orthogonal Laurent polynomials on the unit circle |
| topic | Mixed-type multiple orthogonal Laurent polynomials Unit circle Christoffel-Darboux formulas ABC theorem Recurrence relations Christoffel perturbations Geronimus perturbations Matemáticas Mathematics |
| topic_facet | Mixed-type multiple orthogonal Laurent polynomials Unit circle Christoffel-Darboux formulas ABC theorem Recurrence relations Christoffel perturbations Geronimus perturbations Matemáticas Mathematics |
| url | http://hdl.handle.net/10017/68062 https://dx.doi.org/10.1016/j.cam.2025.117037 |