2024/11/25 by Manuel Mañas, Mañas, Manuel, Miguel Rojas +1 · 2 citations
Mathematics · #33C45 #33C47 #42C05 #47B36 #47B39 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2411.16022
openalex publication_date 2024/11/25 · openalex created_date 2024/12/04 · openalex updated_date 2026/07/28
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.