Harmonic analysis on the proper velocity gyrogroup

Ferreira, Milton

Publication

Harmonic analysis on the proper velocity gyrogroup

2017Journal article

dc.contributor.author	Ferreira, Milton
dc.date.accessioned	2019-02-06T17:00:12Z
dc.date.available	2019-02-06T17:00:12Z
dc.date.issued	2017
dc.description.abstract	In this paper we study harmonic analysis on the Proper Velocity (PV) gyrogroup using the gyrolanguage of analytic hyperbolic geometry. PV addition is the relativistic addition of proper velocities in special relativity and it is related with the hyperboloid model of hyperbolic geometry. The generalized harmonic analysis depends on a complex parameter $z$ and on the radius $t$ of the hyperboloid and comprises the study of the generalized translation operator, the associated convolution operator, the generalized Laplace-Beltrami operator, and its eigenfunctions, the generalized Poisson transform, and its inverse, the generalized Helgason-Fourier transform, its inverse and Plancherel's Theorem. In the limit of large $t,$ $t \rightarrow +\infty,$ the generalized harmonic analysis on the hyperboloid 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. Harmonic Analysis on the Proper Velocity gyrogroup, Banach J. Math. Anal., 11(1), 2017, 21-49.	pt_PT
dc.identifier.doi	10.1215/17358787-3721232	pt_PT
dc.identifier.uri	http://hdl.handle.net/10400.8/3804
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.publisher	Duke University Press	pt_PT
dc.relation.publisherversion	https://projecteuclid.org/euclid.bjma/1476841712	pt_PT
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	pt_PT
dc.subject	PV gyrogroup	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	Harmonic analysis on the proper velocity gyrogroup	pt_PT
dc.type	journal article
dspace.entity.type	Publication
oaire.awardURI	info:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04106%2F2013/PT
oaire.citation.conferencePlace	USA	pt_PT
oaire.citation.endPage	49	pt_PT
oaire.citation.issue	1	pt_PT
oaire.citation.startPage	21	pt_PT
oaire.citation.title	Banach Journal of Mathematical Analysis	pt_PT
oaire.citation.volume	11	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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