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/10773/15363 |
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 gyroisomorphism 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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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 gyroisomorphism 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 Kashan2016-03-22T15:24:06Z2016-03-18T00:00:00Z2016-03-18info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15363engFerreira, M.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:RCAAP2024-02-22T11:28:21Zoai:ria.ua.pt:10773/15363Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:43.193925Repositório 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, M. 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, M. |
author_facet |
Ferreira, M. |
author_role |
author |
dc.contributor.author.fl_str_mv |
Ferreira, M. |
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 gyroisomorphism 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 |
2016-03-22T15:24:06Z 2016-03-18T00:00:00Z 2016-03-18 |
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/10773/15363 |
url |
http://hdl.handle.net/10773/15363 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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 |
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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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1799137557272854528 |