Gyroharmonic Analysis on Relativistic Gyrogroups
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.8/3805 |
Resumo: | Einstein, Möbius, and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $\bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis. Although there is an algebraic gyro-isomorphism between the three models we show that there are some differences between them. Our study focus on the translation and convolution operators, eigenfunctions of the Laplace-Beltrami operator, Poisson transform, Fourier-Helgason transform, its inverse, and Plancherel's Theorem. We show that in the limit of large $t,$ $t \rightarrow +\infty,$ the resulting gyroharmonic analysis tends to the standard Euclidean harmonic analysis on ${\mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis. |
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Gyroharmonic Analysis on Relativistic GyrogroupsGyrogroupsGyroharmonic analysisLaplace Beltrami operatorEigenfunctionsGeneralized Helgason-Fourier transformPlancherel’s theoremEinstein, Möbius, and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $\bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis. Although there is an algebraic gyro-isomorphism between the three models we show that there are some differences between them. Our study focus on the translation and convolution operators, eigenfunctions of the Laplace-Beltrami operator, Poisson transform, Fourier-Helgason transform, its inverse, and Plancherel's Theorem. We show that in the limit of large $t,$ $t \rightarrow +\infty,$ the resulting gyroharmonic analysis tends to the standard Euclidean harmonic analysis on ${\mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.University of KashanIC-OnlineFerreira, Milton2019-02-06T17:27:47Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/3805engFerreira M., Gyroharmonic Analysis on Relativistic Gyrogroups, Mathematics Interdisciplinary Research, 1, 2016, 69-109.2538-36392476-496510.22052/MIR.2016.13908info: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:RCAAP2024-01-17T15:47:58Zoai:iconline.ipleiria.pt:10400.8/3805Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:47:50.307481Repositório 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 |
Gyroharmonic Analysis on Relativistic Gyrogroups |
title |
Gyroharmonic Analysis on Relativistic Gyrogroups |
spellingShingle |
Gyroharmonic Analysis on Relativistic Gyrogroups Ferreira, Milton Gyrogroups Gyroharmonic analysis Laplace Beltrami operator Eigenfunctions Generalized Helgason-Fourier transform Plancherel’s theorem |
title_short |
Gyroharmonic Analysis on Relativistic Gyrogroups |
title_full |
Gyroharmonic Analysis on Relativistic Gyrogroups |
title_fullStr |
Gyroharmonic Analysis on Relativistic Gyrogroups |
title_full_unstemmed |
Gyroharmonic Analysis on Relativistic Gyrogroups |
title_sort |
Gyroharmonic Analysis on Relativistic Gyrogroups |
author |
Ferreira, Milton |
author_facet |
Ferreira, Milton |
author_role |
author |
dc.contributor.none.fl_str_mv |
IC-Online |
dc.contributor.author.fl_str_mv |
Ferreira, Milton |
dc.subject.por.fl_str_mv |
Gyrogroups Gyroharmonic analysis Laplace Beltrami operator Eigenfunctions Generalized Helgason-Fourier transform Plancherel’s theorem |
topic |
Gyrogroups Gyroharmonic analysis Laplace Beltrami operator Eigenfunctions Generalized Helgason-Fourier transform Plancherel’s theorem |
description |
Einstein, Möbius, and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $\bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis. Although there is an algebraic gyro-isomorphism between the three models we show that there are some differences between them. Our study focus on the translation and convolution operators, eigenfunctions of the Laplace-Beltrami operator, Poisson transform, Fourier-Helgason transform, its inverse, and Plancherel's Theorem. We show that in the limit of large $t,$ $t \rightarrow +\infty,$ the resulting gyroharmonic analysis tends to the standard Euclidean harmonic analysis on ${\mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 2016-01-01T00:00:00Z 2019-02-06T17:27:47Z |
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/10400.8/3805 |
url |
http://hdl.handle.net/10400.8/3805 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ferreira M., Gyroharmonic Analysis on Relativistic Gyrogroups, Mathematics Interdisciplinary Research, 1, 2016, 69-109. 2538-3639 2476-4965 10.22052/MIR.2016.13908 |
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 |
University of Kashan |
publisher.none.fl_str_mv |
University of Kashan |
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 |
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1799136972141232128 |