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Banded totally positive matrices and normality for mixed multiple orthogonal polynomials

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arxiv 2404.13965 v1 pith:XAUEABQW submitted 2024-04-22 math.CA math-phmath.MP

Amílcar Branquinho , Ana Foulquié-Moreno , Manuel Mañas This is my paper · ORCID
classification math.CAmath-phmath.MP
keywords polynomialsmatricesnormalitypositiveassociatedbandedlinemixed
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This paper serves as an introduction to banded totally positive matrices, exploring various characterizations and associated properties. A significant result within is the demonstration that the collection of such matrices forms a semigroup, notably including a subset permitting positive bidiagonal factorization. Moreover, the paper applies this concept to investigate step line normality concerning the degrees of associated recursion polynomials. It presents a spectral Favard theorem, ensuring the existence of measures, thereby guaranteeing that these recursion polynomials represent mixed multiple orthogonal polynomials that maintain normality on the step line indices.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mixed Multiple Orthogonal Laurent Polynomials on the Unit Circle

    math.CA 2024-11 conditional novelty 7.0 of 10

    A Gauss-Borel factorization of a rectangular moment matrix yields the first systematic framework for mixed multiple orthogonal Laurent polynomials on the unit circle, with Christoffel and Geronimus perturbation formulas.

  2. Positive Bidiagonal Factorizations for Banded Markov Processes

    math.CA 2026-08 conditional novelty 6.0 of 10

    Positive bidiagonal factorizations turn banded Markov kernels into ordered urn experiments and yield Karlin-McGregor type spectral formulas without reversibility.

  3. General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials

    math.CA 2024-11 conditional novelty 6.0 of 10

    For mixed multiple orthogonal polynomials, the paper derives Christoffel-type formulas for general Geronimus perturbations and proves that the perturbed orthogonality exists exactly when certain tau-determinants do no...

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