A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/15219 |
Resumo: | Recently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of Hypercomplex Function Theory (Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory, 12 (2012), no. 2, 371-391). This paper deals with an extension of that approach to a recurrence relation for the construction of a complete system of orthogonal Clifford-algebra valued polynomials of arbitrary degree. At the same time the matrix approach sheds new light on results about systems of Clifford algebra-valued orthogonal polynomials obtained by Gurlebeck, Bock, Lavika, Delanghe et al. during the last five years. In fact, it allows to prove directly some intrinsic properties of the building blocks essential in the construction process, but not studied so far. |
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A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomialsClifford AnalysisGeneralized Appell polynomialsRecurrence relationsRecently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of Hypercomplex Function Theory (Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory, 12 (2012), no. 2, 371-391). This paper deals with an extension of that approach to a recurrence relation for the construction of a complete system of orthogonal Clifford-algebra valued polynomials of arbitrary degree. At the same time the matrix approach sheds new light on results about systems of Clifford algebra-valued orthogonal polynomials obtained by Gurlebeck, Bock, Lavika, Delanghe et al. during the last five years. In fact, it allows to prove directly some intrinsic properties of the building blocks essential in the construction process, but not studied so far.Springer Basel2016-02-27T12:49:21Z2014-12-01T00:00:00Z2014-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15219eng0188-700910.1007/s00006-014-0505-xCação, IFalcão, M. I.Malonek, H. R.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:28:05Zoai:ria.ua.pt:10773/15219Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:37.584288Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
title |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
spellingShingle |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials Cação, I Clifford Analysis Generalized Appell polynomials Recurrence relations |
title_short |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
title_full |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
title_fullStr |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
title_full_unstemmed |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
title_sort |
A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials |
author |
Cação, I |
author_facet |
Cação, I Falcão, M. I. Malonek, H. R. |
author_role |
author |
author2 |
Falcão, M. I. Malonek, H. R. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Cação, I Falcão, M. I. Malonek, H. R. |
dc.subject.por.fl_str_mv |
Clifford Analysis Generalized Appell polynomials Recurrence relations |
topic |
Clifford Analysis Generalized Appell polynomials Recurrence relations |
description |
Recently, the authors developed a matrix approach to multivariate polynomial sequences by using methods of Hypercomplex Function Theory (Matrix representations of a basic polynomial sequence in arbitrary dimension. Comput. Methods Funct. Theory, 12 (2012), no. 2, 371-391). This paper deals with an extension of that approach to a recurrence relation for the construction of a complete system of orthogonal Clifford-algebra valued polynomials of arbitrary degree. At the same time the matrix approach sheds new light on results about systems of Clifford algebra-valued orthogonal polynomials obtained by Gurlebeck, Bock, Lavika, Delanghe et al. during the last five years. In fact, it allows to prove directly some intrinsic properties of the building blocks essential in the construction process, but not studied so far. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-12-01T00:00:00Z 2014-12 2016-02-27T12:49:21Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/15219 |
url |
http://hdl.handle.net/10773/15219 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0188-7009 10.1007/s00006-014-0505-x |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer Basel |
publisher.none.fl_str_mv |
Springer Basel |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137555952697344 |