A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis

Detalhes bibliográficos
Autor(a) principal: Cação, Isabel
Data de Publicação: 2021
Outros Autores: Falcão, M. I., Malonek, Helmuth R., Tomaz, Graça
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/82543
Resumo: The paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences Vn, first encountered as a special sequence (corresponding to n=2) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for Vn, and we derive an exponential generating function of Vn expressed by Kummer's confluent hypergeometric function.
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spelling A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysisClifford algebraHypercomplex analysisSturm-Liouville equationVietoris' numbersCiências Naturais::MatemáticasScience & TechnologyThe paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences Vn, first encountered as a special sequence (corresponding to n=2) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for Vn, and we derive an exponential generating function of Vn expressed by Kummer's confluent hypergeometric function.This work was supported by Portuguese funds through the CMAT—Research Centre of Mathematics of University of Minho—and through the CIDMA-Center of Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT - Fundação para a Ciência e Tecnologia”), within projects UIDB/00013/2020, UIDP/00013/2020, UIDB/04106/2020 , and UIDP/04106/2020.WileyUniversidade do MinhoCação, IsabelFalcão, M. I.Malonek, Helmuth R.Tomaz, Graça2021-08-092021-08-09T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/82543engCaçao, I, Falcão, M I, Malonek, H R, Tomaz, G. A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis. Math Meth Appl Sci. 2021; 1- 26. https://doi.org/10.1002/mma.76840170-42141099-147610.1002/mma.7684https://onlinelibrary.wiley.com/doi/10.1002/mma.7684info: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:RCAAP2023-10-21T01:24:39Zoai:repositorium.sdum.uminho.pt:1822/82543Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:27:25.621271Repositório 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 Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
title A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
spellingShingle A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
Cação, Isabel
Clifford algebra
Hypercomplex analysis
Sturm-Liouville equation
Vietoris' numbers
Ciências Naturais::Matemáticas
Science & Technology
title_short A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
title_full A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
title_fullStr A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
title_full_unstemmed A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
title_sort A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis
author Cação, Isabel
author_facet Cação, Isabel
Falcão, M. I.
Malonek, Helmuth R.
Tomaz, Graça
author_role author
author2 Falcão, M. I.
Malonek, Helmuth R.
Tomaz, Graça
author2_role author
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.
Tomaz, Graça
dc.subject.por.fl_str_mv Clifford algebra
Hypercomplex analysis
Sturm-Liouville equation
Vietoris' numbers
Ciências Naturais::Matemáticas
Science & Technology
topic Clifford algebra
Hypercomplex analysis
Sturm-Liouville equation
Vietoris' numbers
Ciências Naturais::Matemáticas
Science & Technology
description The paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences Vn, first encountered as a special sequence (corresponding to n=2) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for Vn, and we derive an exponential generating function of Vn expressed by Kummer's confluent hypergeometric function.
publishDate 2021
dc.date.none.fl_str_mv 2021-08-09
2021-08-09T00:00:00Z
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 https://hdl.handle.net/1822/82543
url https://hdl.handle.net/1822/82543
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Caçao, I, Falcão, M I, Malonek, H R, Tomaz, G. A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis. Math Meth Appl Sci. 2021; 1- 26. https://doi.org/10.1002/mma.7684
0170-4214
1099-1476
10.1002/mma.7684
https://onlinelibrary.wiley.com/doi/10.1002/mma.7684
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 Wiley
publisher.none.fl_str_mv Wiley
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
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