Spherical continuous wavelet transforms arising from sections of the Lorentz group

Ferreira, Milton

Publication

Spherical continuous wavelet transforms arising from sections of the Lorentz group

2009-03Journal article

dc.contributor.author	Ferreira, Milton
dc.date.accessioned	2019-02-07T15:49:46Z
dc.date.available	2019-02-07T15:49:46Z
dc.date.issued	2009-03
dc.description.abstract	We consider the conformal group of the unit sphere Sn−1, the so-called proper Lorentz group Spin+(1,n), for the study of spherical continuous wavelet transforms. Our approach is based on the method for construction of general coherent states associated to square integrable group representations over homogeneous spaces. The underlying homogeneous space is an extension to the whole of the group Spin+(1,n) of the factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. Sections on it are constituted by rotations of the subgroup Spin(n) and Möbius transformations of the type ϕa(x) = (x −a)(1 + ax)−1, where a belongs to a given section on a quotient space of the unit ball. This extends in a natural way the work of Antoine and Vandergheynst to anisotropic conformal dilations on the unit sphere.	pt_PT
dc.description.version	info:eu-repo/semantics/publishedVersion	pt_PT
dc.identifier.citation	Ferreira M., Spherical Continuous wavelet transforms arising from sections of the Lorentz group, Appl. Comput. Harmon. Anal. 26 (2) (2009), 212-229	pt_PT
dc.identifier.doi	10.1016/j.acha.2008.04.005	pt_PT
dc.identifier.issn	1063-5203
dc.identifier.other	1096-603X
dc.identifier.uri	http://hdl.handle.net/10400.8/3820
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.publisher	Elsevier	pt_PT
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S1063520308000523	pt_PT
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	pt_PT
dc.subject	Spherical continuous wavelet transform	pt_PT
dc.subject	Gyrogroups	pt_PT
dc.subject	Quotient spaces	pt_PT
dc.subject	Homogeneous spaces	pt_PT
dc.subject	Sections	pt_PT
dc.subject	Anisotropic dilations	pt_PT
dc.title	Spherical continuous wavelet transforms arising from sections of the Lorentz group	pt_PT
dc.type	journal article
dspace.entity.type	Publication
oaire.awardURI	info:eu-repo/grantAgreement/FCT/SFRH/SFRH%2FBD%2F12744%2F2003/PT
oaire.citation.endPage	229	pt_PT
oaire.citation.issue	2	pt_PT
oaire.citation.startPage	212	pt_PT
oaire.citation.title	Applied and Computational Harmonic Analysis	pt_PT
oaire.citation.volume	26	pt_PT
oaire.fundingStream	SFRH
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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