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Mathematics > Classical Analysis and ODEs

arXiv:2411.10834 (math)
[Submitted on 16 Nov 2024]

Title:Mixed Multiple Orthogonal Laurent Polynomials on the Unit Circle

Authors:Edmundo J. Huertas, Manuel Mañas
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Abstract: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.
Comments: 48 pages
Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph); Complex Variables (math.CV)
MSC classes: 33C45, 33C47, 42C05, 15A23
Cite as: arXiv:2411.10834 [math.CA]
  (or arXiv:2411.10834v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2411.10834

Submission history

From: Manuel Mañas [view email]
[v1] Sat, 16 Nov 2024 16:33:52 UTC (46 KB)
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