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General geronimus perturbations for mixed multiple orthogonal polynomials Mañas Baena, Manuel Enrique Rojas Gómez, Miguel Ángel 51-73 Mixed multiple orthogonal polynomials Geronimus perturbations Christoffel formulas Spectral theory of matrix polynomials Física matemática 2212 Física Teórica 2025 Acuerdos Transformativos CRUE-CSIC General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied through both right and left multiplication to a rectangular matrix of measures associated with mixed multiple orthogonal polynomials. These transformations produce Christoffel-type formulas that establish relationships between the perturbed and original polynomials. Moreover, it is proven that the existence of Geronimus-perturbed orthogonality is equivalent to the non-cancellation of certain τ -determinants. The effect of these transformations on the Markov-Stieltjes matrix functions is also determined. As a case study, we examine the Jacobi–Piñeiro orthogonal polynomials with three weights. Ministerio de Ciencia, Innovación y Universidades (España) Agencia Estatal de Investigación (España) European Commission Depto. de Física Teórica Fac. de Ciencias Físicas TRUE pub 2025-10-02T18:30:01Z 2025-10-02T18:30:01Z 2025-04-05 journal article VoR https://hdl.handle.net/20.500.14352/124486 1664-2368 10.1007/s13324-025-01036-y 1664-235X eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-122154NB-I00/ES/ORTOGONALIDAD Y APROXIMACION CON APLICACIONES EN MACHINE LEARNING Y TEORIA DE LA PROBABILIDAD/ Mañas, M., Rojas, M. General geronimus perturbations for mixed multiple orthogonal polynomials. Anal.Math.Phys. 15, 50 (2025). https://doi.org/10.1007/s13324-025-01036-y Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ open access application/pdf application/pdf Springer