Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One
Autor(a) principal: | |
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Data de Publicação: | 2019 |
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/10314/5210 |
Resumo: | Fundamentals of a function theory in co-dimension one for Clifford algebra valued functions over R^n+1 are considered. Special attention is given to their origins in analytic properties of holomorphic functions of one and, by some duality reasons, also of several complex variables. Due to algebraic peculiarities caused by non-commutativity of the Clifford product, generalized holomorphic functions are characterized by two different but equivalent properties: on one side by local derivability (existence of a well-defined derivative related to co-dimension one) and on the other side by differentiability (existence of a local approximation by linear mappings related to dimension one). As important applications, sequences of harmonic Appell polynomials are considered whose definition and explicit analytic representations rely essentially on both dual approaches. |
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Harmonic Analysis and Hypercomplex Function Theory in Co-dimension OneClifford algebrasHypercomplex differential formsHypercomplex derivativeHypercomplex Appell polynomialsFundamentals of a function theory in co-dimension one for Clifford algebra valued functions over R^n+1 are considered. Special attention is given to their origins in analytic properties of holomorphic functions of one and, by some duality reasons, also of several complex variables. Due to algebraic peculiarities caused by non-commutativity of the Clifford product, generalized holomorphic functions are characterized by two different but equivalent properties: on one side by local derivability (existence of a well-defined derivative related to co-dimension one) and on the other side by differentiability (existence of a local approximation by linear mappings related to dimension one). As important applications, sequences of harmonic Appell polynomials are considered whose definition and explicit analytic representations rely essentially on both dual approaches.Springer2021-06-28T02:43:35Z2021-06-282019-08-29T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10314/5210http://hdl.handle.net/10314/5210eng978-3-030-26747-6Malonek, H.R.Cação, I.Falcão, M.I.Tomaz, G.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:RCAAP2024-01-14T02:59:31Zoai:bdigital.ipg.pt:10314/5210Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:44:01.632297Repositório 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 |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
title |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
spellingShingle |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One Malonek, H.R. Clifford algebras Hypercomplex differential forms Hypercomplex derivative Hypercomplex Appell polynomials |
title_short |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
title_full |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
title_fullStr |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
title_full_unstemmed |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
title_sort |
Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One |
author |
Malonek, H.R. |
author_facet |
Malonek, H.R. Cação, I. Falcão, M.I. Tomaz, G. |
author_role |
author |
author2 |
Cação, I. Falcão, M.I. Tomaz, G. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Malonek, H.R. Cação, I. Falcão, M.I. Tomaz, G. |
dc.subject.por.fl_str_mv |
Clifford algebras Hypercomplex differential forms Hypercomplex derivative Hypercomplex Appell polynomials |
topic |
Clifford algebras Hypercomplex differential forms Hypercomplex derivative Hypercomplex Appell polynomials |
description |
Fundamentals of a function theory in co-dimension one for Clifford algebra valued functions over R^n+1 are considered. Special attention is given to their origins in analytic properties of holomorphic functions of one and, by some duality reasons, also of several complex variables. Due to algebraic peculiarities caused by non-commutativity of the Clifford product, generalized holomorphic functions are characterized by two different but equivalent properties: on one side by local derivability (existence of a well-defined derivative related to co-dimension one) and on the other side by differentiability (existence of a local approximation by linear mappings related to dimension one). As important applications, sequences of harmonic Appell polynomials are considered whose definition and explicit analytic representations rely essentially on both dual approaches. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-08-29T00:00:00Z 2021-06-28T02:43:35Z 2021-06-28 |
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/10314/5210 http://hdl.handle.net/10314/5210 |
url |
http://hdl.handle.net/10314/5210 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
978-3-030-26747-6 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
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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1799136935890911232 |