A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials

Detalhes bibliográficos
Autor(a) principal: Cação, I.
Data de Publicação: 2014
Outros Autores: Falcão, M. I., Malonek, H. R.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/31229
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 Guerlebeck, Bock, Lavicka, 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.
id RCAP_7617a4f4f7a2890cf572b082e03cef52
oai_identifier_str oai:repositorium.sdum.uminho.pt:1822/31229
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomialsClifford AnalysisGeneralized Appell polynomialsRecurrence relationsScience & TechnologyRecently, 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 Guerlebeck, Bock, Lavicka, 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.Fundação para a Ciência e a Tecnologia (FCT)Springer VerlagUniversidade do MinhoCação, I.Falcão, M. I.Malonek, H. R.20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/31229eng0188-700910.1007/s00006-014-0505-xhttp://link.springer.cominfo: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:RCAAP2023-07-21T12:29:04Zoai:repositorium.sdum.uminho.pt:1822/31229Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:23:59.029143Repositório 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
Science & Technology
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.none.fl_str_mv Universidade do Minho
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
Science & Technology
topic Clifford Analysis
Generalized Appell polynomials
Recurrence relations
Science & Technology
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 Guerlebeck, Bock, Lavicka, 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
2014-01-01T00:00:00Z
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/1822/31229
url http://hdl.handle.net/1822/31229
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0188-7009
10.1007/s00006-014-0505-x
http://link.springer.com
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 Verlag
publisher.none.fl_str_mv Springer Verlag
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
instname_str 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
repository.mail.fl_str_mv
_version_ 1799132717531529216

Registros relacionados