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Vector Interpretation of the Matrix Orthogonality on the Real Line

2009-10-12Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorBranquinho, A.
dc.contributor.authorMarcellán, F.
dc.contributor.authorMendes, A.
dc.date.accessioned2025-11-05T12:06:05Z
dc.date.available2025-11-05T12:06:05Z
dc.date.issued2009-10-12
dc.descriptionFonte: https://arxiv.org/abs/0910.1737
dc.description.abstractIn this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed. Finally, a Markov's type theorem is presented.eng
dc.description.sponsorshipThe work of the second author (FM) has been supported by Direccíon General de Investigacíon, Ministerio de Ciencia e Innovacíon of Spain, under grant MTM2009-12740-C03-01.
dc.identifier.citationBranquinho, Amílcar & Marcellán, Francisco & Mendes, A.. (2009). Vector Interpretation of the Matrix Orthogonality on the Real Line. Acta Applicandae Mathematicae. DOI: https://doi.org/112. 10.1007/s10440-010-9577-3.
dc.identifier.doi10.1007/s10440-010-9577-3
dc.identifier.eissn1572-9036
dc.identifier.issn0167-8019
dc.identifier.urihttp://hdl.handle.net/10400.8/14518
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s10440-010-9577-3
dc.relation.ispartofActa Applicandae Mathematicae
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectMatrix orthogonal polynomials
dc.subjectproblems of Hermite-Pad´e
dc.subjectlinear func- tional
dc.subjectrecurrence relation
dc.subjecttridiagonal operator
dc.subjectFavard theorem
dc.subjectasymptotic results
dc.subjectNevai class
dc.titleVector Interpretation of the Matrix Orthogonality on the Real Lineeng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage27
oaire.citation.startPage1
oaire.citation.titleActa Applicandae Mathematicae
oaire.versionhttp://purl.org/coar/version/c_ab4af688f83e57aa
person.familyNameMendes
person.givenNameAna
person.identifier.ciencia-id3C19-42EA-DDBD
person.identifier.orcid0000-0002-4161-6130
person.identifier.scopus-author-id55873199300
relation.isAuthorOfPublication3523e160-c260-47a6-89cc-eb3fca0059d9
relation.isAuthorOfPublication.latestForDiscovery3523e160-c260-47a6-89cc-eb3fca0059d9

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In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed. Finally, a Markov's type theorem is presented.
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