Matrix approach to hypercomplex Appell polynomials

Bibliographic Details
Main Author: Aceto, Lídia
Publication Date: 2017
Other Authors: Malonek, Helmuth R., Tomaz, Graça
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/21347
Summary: Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a suitable first order initial value problem. The paper aims to confirm that the unifying character of this approach can also be applied to the construction of homogeneous Appell polynomials that are solutions of a generalized Cauchy–Riemann system in Euclidean spaces of arbitrary dimension. The result contributes to the development of techniques for polynomial approximation and interpolation in non-commutative Hypercomplex Function Theories with Clifford algebras.
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spelling Matrix approach to hypercomplex Appell polynomialsHypercomplex differentiabilityAppell polynomialsCreation matrixPascal matrixRecently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a suitable first order initial value problem. The paper aims to confirm that the unifying character of this approach can also be applied to the construction of homogeneous Appell polynomials that are solutions of a generalized Cauchy–Riemann system in Euclidean spaces of arbitrary dimension. The result contributes to the development of techniques for polynomial approximation and interpolation in non-commutative Hypercomplex Function Theories with Clifford algebras.Elsevier2018-01-05T16:36:43Z2017-01-01T00:00:00Z2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/21347eng0168-927410.1016/j.apnum.2016.07.006Aceto, LídiaMalonek, Helmuth R.Tomaz, Graçainfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:11:02Zoai:ria.ua.pt:10773/21347Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:00:06.267141Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Matrix approach to hypercomplex Appell polynomials
title Matrix approach to hypercomplex Appell polynomials
spellingShingle Matrix approach to hypercomplex Appell polynomials
Aceto, Lídia
Hypercomplex differentiability
Appell polynomials
Creation matrix
Pascal matrix
title_short Matrix approach to hypercomplex Appell polynomials
title_full Matrix approach to hypercomplex Appell polynomials
title_fullStr Matrix approach to hypercomplex Appell polynomials
title_full_unstemmed Matrix approach to hypercomplex Appell polynomials
title_sort Matrix approach to hypercomplex Appell polynomials
author Aceto, Lídia
author_facet Aceto, Lídia
Malonek, Helmuth R.
Tomaz, Graça
author_role author
author2 Malonek, Helmuth R.
Tomaz, Graça
author2_role author
author
dc.contributor.author.fl_str_mv Aceto, Lídia
Malonek, Helmuth R.
Tomaz, Graça
dc.subject.por.fl_str_mv Hypercomplex differentiability
Appell polynomials
Creation matrix
Pascal matrix
topic Hypercomplex differentiability
Appell polynomials
Creation matrix
Pascal matrix
description Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a suitable first order initial value problem. The paper aims to confirm that the unifying character of this approach can also be applied to the construction of homogeneous Appell polynomials that are solutions of a generalized Cauchy–Riemann system in Euclidean spaces of arbitrary dimension. The result contributes to the development of techniques for polynomial approximation and interpolation in non-commutative Hypercomplex Function Theories with Clifford algebras.
publishDate 2017
dc.date.none.fl_str_mv 2017-01-01T00:00:00Z
2017
2018-01-05T16:36:43Z
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/10773/21347
url http://hdl.handle.net/10773/21347
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0168-9274
10.1016/j.apnum.2016.07.006
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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