Bidiagonal matrix factorisations related to multiple orthogonal polynomials

Autor:	Branquinho, Amílcar, Díaz, Juan E. F., Foulquié-Moreno, Ana, Lima, Hélder, Mañas, Manuel
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs 15A23 33C45 42C05 47B36. (Primary) 11J70 33C20. (Secondary)
Druh dokumentu:	Working Paper
Popis:	In this work, we develop two methods to obtain a factorisation as a product of bidiagonal matrices for the Hessenberg recurrence matrix of a system of multiple orthogonal polynomials. One method is based on the Gauss-Borel factorisation of the moment matrix of the system and of its Darboux transformations, and the other uses the connection of multiple orthogonal polynomials with production matrices and branched continued fractions. As a case study, we present an explicit bidiagonal factorisation for the Hessenberg recurrence matrix of the Jacobi-Pi\~neiro polynomials, using both methods, and of the multiple Laguerre polynomials of first kind, as a limiting case. Comment: 22 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.03694 Zobrazit plný text záznamu View this record from Arxiv