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Title: Gyroharmonic analysis on relativistic gyrogroups
Author: Ferreira, M.
Keywords: Gyrogroups
Gyroharmonic Analysis
Laplace Beltrami operator
Generalized Helgason-Fourier transform
Plancherel's Theorem
Issue Date: 18-Mar-2016
Publisher: University of Kashan
Abstract: Einstein, Möbius, and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $\bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis. Although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. Our study focus on the translation and convolution operators, eigenfunctions of the Laplace-Beltrami operator, Poisson transform, Fourier-Helgason transform, its inverse, and Plancherel's Theorem. We show that in the limit of large $t,$ $t \rightarrow +\infty,$ the resulting gyroharmonic analysis tends to the standard Euclidean harmonic analysis on ${\mathbb R}^n,$ thus unifying hyperbolic and Euclidean harmonic analysis.
Peer review: yes
Publisher Version:
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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