On the Π-operator in Clifford analysis

Detalhes bibliográficos
Autor(a) principal: Blaya, Ricardo Abreu
Data de Publicação: 2016
Outros Autores: Reyes, Juan Bory, Adán, Alí Guzmán, Kähler, Uwe
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/15004
Resumo: In this paper we prove that a generalization of complex Π-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism.
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spelling On the Π-operator in Clifford analysisClifford analysisTeodorescu transformΠ-operatorIntegral representationsIn this paper we prove that a generalization of complex Π-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism.Elsevier2018-07-20T14:00:51Z2016-02-15T00:00:00Z2016-02-152017-02-14T15:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15004eng0022-247X10.1016/j.jmaa.2015.09.038Blaya, Ricardo AbreuReyes, Juan BoryAdán, Alí GuzmánKähler, Uweinfo: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:RCAAP2024-02-22T11:27:41Zoai:ria.ua.pt:10773/15004Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:28.386166Repositório 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 On the Π-operator in Clifford analysis
title On the Π-operator in Clifford analysis
spellingShingle On the Π-operator in Clifford analysis
Blaya, Ricardo Abreu
Clifford analysis
Teodorescu transform
Π-operator
Integral representations
title_short On the Π-operator in Clifford analysis
title_full On the Π-operator in Clifford analysis
title_fullStr On the Π-operator in Clifford analysis
title_full_unstemmed On the Π-operator in Clifford analysis
title_sort On the Π-operator in Clifford analysis
author Blaya, Ricardo Abreu
author_facet Blaya, Ricardo Abreu
Reyes, Juan Bory
Adán, Alí Guzmán
Kähler, Uwe
author_role author
author2 Reyes, Juan Bory
Adán, Alí Guzmán
Kähler, Uwe
author2_role author
author
author
dc.contributor.author.fl_str_mv Blaya, Ricardo Abreu
Reyes, Juan Bory
Adán, Alí Guzmán
Kähler, Uwe
dc.subject.por.fl_str_mv Clifford analysis
Teodorescu transform
Π-operator
Integral representations
topic Clifford analysis
Teodorescu transform
Π-operator
Integral representations
description In this paper we prove that a generalization of complex Π-operator in Clifford analysis, obtained by the use of two orthogonal bases of a Euclidean space, possesses several mapping and invertibility properties, as studied before for quaternion-valued functions as well as in the standard Clifford analysis setting. We improve and generalize most of those previous results in this direction and additionally other consequent results are presented. In particular, the expression of the jump of the generalized Π-operator across the boundary of the domain is obtained as well as an estimate for the norm of the Π-operator is given. At the end an application of the generalized Π-operator to the solution of Beltrami equations is studied where we give conditions for a solution to realize a local and global homeomorphism.
publishDate 2016
dc.date.none.fl_str_mv 2016-02-15T00:00:00Z
2016-02-15
2017-02-14T15:00:00Z
2018-07-20T14:00:51Z
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/10773/15004
url http://hdl.handle.net/10773/15004
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-247X
10.1016/j.jmaa.2015.09.038
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
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