Mañas Baena, Manuel EnriqueRojas Gómez, Miguel Ángel2025-10-022025-10-022025-04-05Mañas, 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-y1664-236810.1007/s13324-025-01036-yhttps://hdl.handle.net/20.500.14352/1244862025 Acuerdos Transformativos CRUE-CSICGeneral 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal article1664-235Xhttps//doi.org/10.1007/s13324-025-01036-yhttps://link.springer.com/article/10.1007/s13324-025-01036-yopen access51-73Mixed multiple orthogonal polynomialsGeronimus perturbationsChristoffel formulasSpectral theory of matrix polynomialsFísica matemática2212 Física Teórica