Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/35239
Title: | Multiple orthogonal polynomials: pearson equations and Christoffel formulas |
Author: | Branquinho, Amílcar Foulquié-Moreno, Ana Mañas, Manuel |
Keywords: | Multiple orthogonal polynomials Banded tetradiagonal recursion matrices Christoffel transformations Geronimus transformations Pearson equation |
Issue Date: | 3-Oct-2022 |
Publisher: | Birkhauser |
Abstract: | 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–Piñeiro 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–Piñeiro 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 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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/35239 |
DOI: | 10.1007/s13324-022-00734-1 |
ISSN: | 1664-2368 |
Publisher Version: | https://link.springer.com/article/10.1007/s13324-022-00734-1 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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s13324-022-00734-1.pdf | 1.25 MB | Adobe PDF | View/Open |
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