Publicação
Gyroharmonic Analysis on Relativistic Gyrogroups
| dc.contributor.author | Ferreira, Milton | |
| dc.date.accessioned | 2019-02-06T17:27:47Z | |
| dc.date.available | 2019-02-06T17:27:47Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | 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. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Ferreira M., Gyroharmonic Analysis on Relativistic Gyrogroups, Mathematics Interdisciplinary Research, 1, 2016, 69-109. | pt_PT |
| dc.identifier.doi | 10.22052/MIR.2016.13908 | pt_PT |
| dc.identifier.issn | 2538-3639 | |
| dc.identifier.other | 2476-4965 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/3805 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | University of Kashan | pt_PT |
| dc.relation.publisherversion | http://mir.kashanu.ac.ir/article_13908.html | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | Gyrogroups | pt_PT |
| dc.subject | Gyroharmonic analysis | pt_PT |
| dc.subject | Laplace Beltrami operator | pt_PT |
| dc.subject | Eigenfunctions | pt_PT |
| dc.subject | Generalized Helgason-Fourier transform | pt_PT |
| dc.subject | Plancherel’s theorem | pt_PT |
| dc.title | Gyroharmonic Analysis on Relativistic Gyrogroups | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardNumber | UID/MAT/04106/2013 | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04106%2F2013/PT | |
| oaire.citation.endPage | 109 | pt_PT |
| oaire.citation.issue | 1 | pt_PT |
| oaire.citation.startPage | 69 | pt_PT |
| oaire.citation.title | Mathematics Interdisciplinary Research | pt_PT |
| oaire.citation.volume | 1 | pt_PT |
| oaire.fundingStream | 5876 | |
| person.familyName | Ferreira | |
| person.givenName | Milton | |
| person.identifier.ciencia-id | CA19-2009-F26D | |
| person.identifier.orcid | 0000-0003-1816-8293 | |
| person.identifier.rid | A-2004-2015 | |
| person.identifier.scopus-author-id | 12144179800 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | b1460cdc-4ced-46c6-a637-68b425d104dc | |
| relation.isAuthorOfPublication.latestForDiscovery | b1460cdc-4ced-46c6-a637-68b425d104dc | |
| relation.isProjectOfPublication | d62eccf5-8596-4ba5-afab-f0f258cfd08e | |
| relation.isProjectOfPublication.latestForDiscovery | d62eccf5-8596-4ba5-afab-f0f258cfd08e |
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