Vietoris' number sequence and its generalizations through hypercomplex function theory

Detalhes bibliográficos
Autor(a) principal: Cação, Isabel
Data de Publicação: 2018
Outros Autores: Falcão, M. I., Malonek, Helmuth R.
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/62819
Resumo: The so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the first time in a celebrated theorem by Vietoris (1958) about the positivity of certain trigonometric sums with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/ Salinas, 2004). In the context of hypercomplex function theory those numbers appear as coefficients of special homogeneous polynomials in R^3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in R^n.
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spelling Vietoris' number sequence and its generalizations through hypercomplex function theoryVietoris' number sequenceMonogenic Appell polynomialsGenerating functionsCiências Naturais::MatemáticasThe so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the first time in a celebrated theorem by Vietoris (1958) about the positivity of certain trigonometric sums with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/ Salinas, 2004). In the context of hypercomplex function theory those numbers appear as coefficients of special homogeneous polynomials in R^3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in R^n.The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013. The work of the other authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEst-OE/MAT/UI4106/2013.Universidade do MinhoCação, IsabelFalcão, M. I.Malonek, Helmuth R.20182018-01-01T00:00:00Zconference paperinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/1822/62819enghttp://elibrary.matf.bg.ac.rs/handle/123456789/4699info: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:RCAAP2024-05-11T04:51:40Zoai:repositorium.sdum.uminho.pt:1822/62819Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T04:51:40Repositório 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 Vietoris' number sequence and its generalizations through hypercomplex function theory
title Vietoris' number sequence and its generalizations through hypercomplex function theory
spellingShingle Vietoris' number sequence and its generalizations through hypercomplex function theory
Cação, Isabel
Vietoris' number sequence
Monogenic Appell polynomials
Generating functions
Ciências Naturais::Matemáticas
title_short Vietoris' number sequence and its generalizations through hypercomplex function theory
title_full Vietoris' number sequence and its generalizations through hypercomplex function theory
title_fullStr Vietoris' number sequence and its generalizations through hypercomplex function theory
title_full_unstemmed Vietoris' number sequence and its generalizations through hypercomplex function theory
title_sort Vietoris' number sequence and its generalizations through hypercomplex function theory
author Cação, Isabel
author_facet Cação, Isabel
Falcão, M. I.
Malonek, Helmuth R.
author_role author
author2 Falcão, M. I.
Malonek, Helmuth R.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Cação, Isabel
Falcão, M. I.
Malonek, Helmuth R.
dc.subject.por.fl_str_mv Vietoris' number sequence
Monogenic Appell polynomials
Generating functions
Ciências Naturais::Matemáticas
topic Vietoris' number sequence
Monogenic Appell polynomials
Generating functions
Ciências Naturais::Matemáticas
description The so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the first time in a celebrated theorem by Vietoris (1958) about the positivity of certain trigonometric sums with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/ Salinas, 2004). In the context of hypercomplex function theory those numbers appear as coefficients of special homogeneous polynomials in R^3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in R^n.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
dc.type.driver.fl_str_mv conference paper
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/62819
url https://hdl.handle.net/1822/62819
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://elibrary.matf.bg.ac.rs/handle/123456789/4699
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.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 mluisa.alvim@gmail.com
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