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http://hdl.handle.net/10773/35239
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DC Field | Value | Language |
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dc.contributor.author | Branquinho, Amílcar | pt_PT |
dc.contributor.author | Foulquié-Moreno, Ana | pt_PT |
dc.contributor.author | Mañas, Manuel | pt_PT |
dc.date.accessioned | 2022-11-21T16:14:49Z | - |
dc.date.available | 2022-11-21T16:14:49Z | - |
dc.date.issued | 2022-10-03 | - |
dc.identifier.issn | 1664-2368 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/35239 | - |
dc.description.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. | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Birkhauser | pt_PT |
dc.relation | UID/MAT/00324/2020 | pt_PT |
dc.relation | UID/MAT/04106/2020 | pt_PT |
dc.relation | PGC2018-096504-B-C33 | pt_PT |
dc.relation | PID2021-122154NB-I00 | pt_PT |
dc.rights | openAccess | pt_PT |
dc.subject | Multiple orthogonal polynomials | pt_PT |
dc.subject | Banded tetradiagonal recursion matrices | pt_PT |
dc.subject | Christoffel transformations | pt_PT |
dc.subject | Geronimus transformations | pt_PT |
dc.subject | Pearson equation | pt_PT |
dc.title | Multiple orthogonal polynomials: pearson equations and Christoffel formulas | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.issue | 6 | pt_PT |
degois.publication.title | Analysis and Mathematical Physics | pt_PT |
degois.publication.volume | 12 | pt_PT |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s13324-022-00734-1 | pt_PT |
dc.identifier.doi | 10.1007/s13324-022-00734-1 | pt_PT |
dc.identifier.essn | 1664-235X | pt_PT |
dc.identifier.articlenumber | 129 | pt_PT |
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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