Logo do repositório
 
Publicação

Harmonic Analysis on the Einstein Gyrogroup

2014Artigo científico Acesso restrito
Ver registo simples
dc.contributor.authorFerreira, Milton
dc.date.accessioned2019-02-07T11:52:17Z
dc.date.available2019-02-07T11:52:17Z
dc.date.issued2014
dc.description.abstractIn this paper we study harmonic analysis on the Einstein gyrogroup of the open ball of ${\mathbb R}^n, n \in \mathbb{N},$ centered at the origin and with arbitrary radius $t \in \mathbb{R}^+,$ associated to the generalised Laplace-Beltrami operator $$ L_{\sigma,t} = \disp \left( 1 - \frac{\|x\|^2}{t^2} \right) \!\left( \Delta - \sum_{i,j=1}^n \frac{x_i x_j}{t^2} \frac{\partial^2}{\partial x_i \partial x_j} - \frac{\kappa}{t^2} \sum_{i=1}^n x_i \frac{\partial}{\partial x_i} + \frac{\kappa(2-\kappa)}{4t^2} \right)$$where $\kappa=n+\sigma$ and $\sigma \in {\mathbb R}$ is an arbitrary parameter. The generalised harmonic analysis for $L_{\sigma,t}$ gives rise to the $(\sigma,t)$-translation, the $(\sigma,t)$-convo\-lution, the $(\sigma,t)$-spherical Fourier transform, the $(\sigma,t)$-Poisson transform, the $(\sigma,t)$-Helgason Fourier transform, its inverse transform and Plancherel's Theorem. In the limit of large $t,$ $t \rightarrow +\infty,$ the resulting hyperbolic harmonic analysis tends to the standard Euclidean harmonic analysis on ${\mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFerreira M., Harmonic analysis on the Einstein gyrogroup, J. Geom. Symm. Phys. 35, 2014, 21-60pt_PT
dc.identifier.doi10.7546/jgsp-35-2014-21-60pt_PT
dc.identifier.issn1312-5192
dc.identifier.other1314-5673
dc.identifier.urihttp://hdl.handle.net/10400.8/3809
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherInstitute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences (IBPhBME-BAS)pt_PT
dc.relation.publisherversionhttps://projecteuclid.org/euclid.jgsp/1495850573pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectEinstein gyrogrouppt_PT
dc.subjectGeneralised Helgason-Fourier transformpt_PT
dc.subjectSpherical functionspt_PT
dc.subjectHyperbolic convolutionpt_PT
dc.subjectEigenfunctionspt_PT
dc.subjectLaplace-Beltrami-operatorpt_PT
dc.titleHarmonic Analysis on the Einstein Gyrogrouppt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/PEst-OE%2FMAT%2FUI4106%2F2014/PT
oaire.citation.endPage60pt_PT
oaire.citation.startPage21pt_PT
oaire.citation.titleJournal of Geometry and Symmetry in Physicspt_PT
oaire.citation.volume35pt_PT
oaire.fundingStream5876
person.familyNameFerreira
person.givenNameMilton
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.orcid0000-0003-1816-8293
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id12144179800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublicationb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isAuthorOfPublication.latestForDiscoveryb1460cdc-4ced-46c6-a637-68b425d104dc
relation.isProjectOfPublicationb4b0f90a-1fc4-4a0e-97d5-f2107ac33ffa
relation.isProjectOfPublication.latestForDiscoveryb4b0f90a-1fc4-4a0e-97d5-f2107ac33ffa

Ficheiros

Principais
A mostrar 1 - 1 de 1
Miniatura indisponível
Nome:
Harm_Anal_Einstein_gyro_Post_Print.pdf
Tamanho:
298.12 KB
Formato:
Adobe Portable Document Format
Descrição:
Ver/Abrir
Licença
A mostrar 1 - 1 de 1
Miniatura indisponível
Nome:
license.txt
Tamanho:
1.32 KB
Formato:
Item-specific license agreed upon to submission
Descrição:
Ver/Abrir

Coleções

ESTG - Artigos em revistas internacionais