2024/11/16 by Edmundo J. Huertas, Huertas, Edmundo J., Manuel Mañas +1
Mathematics · #15A23 #33C45 #33C47 #42C05 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2411.10834
openalex publication_date 2024/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.