Publicação
Harmonic Analysis on the Möbius Gyrogroup
| dc.contributor.author | Ferreira, Milton | |
| dc.date.accessioned | 2019-02-06T16:48:48Z | |
| dc.date.available | 2019-02-06T16:48:48Z | |
| dc.date.issued | 2015-04 | |
| dc.description.abstract | In this paper, we propose to develop harmonic analysis on the Poincaré ball B, a model of then-dimensional real hyperbolic space. The Poincaré ball B is the open ball of the Euclidean n-space $\bkR^n$ with radius t >0, centered at the origin of $\bkR^n$ and equipped with Möbius addition, thus forming a Möbius gyrogroup where Möbius addition in the ball plays the role of vector addition in $\bkR^n.$ For any t>0 and an arbitrary parameter $\sigma \in \bkR$ we study the $(\sigma,t)$-translation, the $(\sigma,t)$-convolution, the eigenfunctions of the $(\sigma,t)$-Laplace-Beltrami operator, the $(\sigma,t)$-Helgason Fourier transform, its inverse transform and the associated Plancherel's Theorem, which represent counterparts of standard tools, thus, enabling an effective theory of hyperbolic harmonic analysis. Moreover, when $t \rightarrow +\infty$ the resulting hyperbolic harmonic analysis on B tends to the standard Euclidean harmonic analysis on $\bkR^n,$ thus unifying hyperbolic and Euclidean harmonic analysis. As an application, we construct diffusive wavelets on B. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Ferreira M., Harmonic analysis on the Möbius gyrogroup, J. Fourier Anal. Appl., 21(2), 2015, 281-317 | pt_PT |
| dc.identifier.doi | 10.1007/s00041-014-9370-1 | pt_PT |
| dc.identifier.issn | 1069-5869 | |
| dc.identifier.other | 1531-5851 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/3803 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer Nature [academic journals on nature.com] | pt_PT |
| dc.relation.publisherversion | https://link.springer.com/article/10.1007%2Fs00041-014-9370-1 | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | Möbius gyrogroup | pt_PT |
| dc.subject | Helgason-Fourier transform | pt_PT |
| dc.subject | Spherical functions | pt_PT |
| dc.subject | Hyperbolic convolution | pt_PT |
| dc.subject | Eigenfunctions of the Laplace-Beltrami-operator | pt_PT |
| dc.subject | Diffusive wavelets | pt_PT |
| dc.title | Harmonic Analysis on the Möbius Gyrogroup | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardNumber | PEst-OE/MAT/UI4106/2014 | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/5876/PEst-OE%2FMAT%2FUI4106%2F2014/PT | |
| oaire.citation.endPage | 317 | pt_PT |
| oaire.citation.issue | 2 | pt_PT |
| oaire.citation.startPage | 281 | pt_PT |
| oaire.citation.title | Journal of Fourier Analysis and Applications | pt_PT |
| oaire.citation.volume | 21 | 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 |
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