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...

Descripción completa

Detalles Bibliográficos
Autores: Huertas Cejudo, Edmundo José|||0000-0001-6802-3303, Mañas Baena, Manuel
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/68062
Acceso en línea:http://hdl.handle.net/10017/68062
https://dx.doi.org/10.1016/j.cam.2025.117037
Access Level:acceso abierto
Palabra clave:Mixed-type multiple orthogonal Laurent polynomials
Unit circle
Christoffel-Darboux formulas
ABC theorem
Recurrence relations
Christoffel perturbations
Geronimus perturbations
Matemáticas
Mathematics
Descripción
Sumario: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.