2026-06-28T04:56:21Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/725702024-08-26T17:21:11Zcom_20.500.14352_14col_20.500.14352_15

Branquinho, Amilcar Foulquié Moreno, Ana Mañas Baena, Manuel Enrique 2023-06-22T12:27:53Z 2023-06-22T12:27:53Z 2022-12 1664-2368 10.1007/s13324-022-00734-1 https://hdl.handle.net/20.500.14352/72570 http://dx.doi.org/10.1007/s13324-022-00734-1 https://link.springer.com/ Multiple orthogonal polynomials with respect to two weights on the step-line are considered. A connection between different dual spectral matrices, one banded (recursion matrix) and one Hessenberg, respectively, and the Gauss-Borel factorization of the moment matrix is given. It is shown a hidden freedom exhibited by the spectral system related to the multiple orthogonal polynomials. Pearson equations are discussed, a Laguerre-Freud matrix is considered, and differential equations for type I and II multiple orthogonal polynomials, as well as for the corresponding linear forms are given. The Jacobi-Pineiro multiple orthogonal polynomials of type I and type II are used as an illustrating case and the corresponding differential relations are presented. A permuting Christoffel transformation is discussed, finding the connection between the different families of multiple orthogonal polynomials. The Jacobi-Pineiro case provides a convenient illustration of these symmetries, giving linear relations between different polynomials with shifted and permuted parameters. We also present the general theory for the perturbation of each weight by a different polynomial or rational function aka called Christoffel and Geronimus transformations. The connections formulas between the type II multiple orthogonal polynomials, the type I linear forms, as well as the vector Stieltjes-Markov vector functions is also presented. We illustrate these findings by analyzing the special case of modification by an even polynomial. eng https://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Multiple orthogonal polynomials: Pearson equations and Christoffel formulas journal article