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...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/133638 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/133638 |
| Access Level: | acceso abierto |
| Palavra-chave: | 530.1 Mixed-type multiple orthogonal Laurent polynomials Unit circle Christoffel–Darboux formulas ABC theorem Recurrence relations Christoffel perturbations Geronimus perturbations Física-Modelos matemáticos 2212 Física Teórica |
| Resumo: | 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. |
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