Repositório Institucional da Universidade de Aveiro > CIDMA - Centro de Investigação e Desenvolvimento em Matemática e Aplicações > CIDMA - Artigos > Harmonic analysis on the proper velocity gyrogroup
 Please use this identifier to cite or link to this item http://hdl.handle.net/10773/16613

 title: Harmonic analysis on the proper velocity gyrogroup authors: Ferreira, Milton keywords: PV gyrogroupLaplace Beltrami operatorEigenfunctionsGeneralized Helgason-Fourier transformPlancherel's Theorem issue date: Jan-2017 publisher: Duke University Press 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. description: Revista sem período de embargo. URI: http://hdl.handle.net/10773/16613 ISSN: 1735-8787 publisher version/DOI: http://projecteuclid.org/euclid.bjma/1476841712 source: Banach Journal of Mathematical Analysis appears in collections CIDMA - Artigos

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