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Paper Information

Journal:   BANACH JOURNAL OF MATHEMATICAL ANALYSIS   2017 , Volume 11 , Number 1; Page(s) 21 To 49.
 
Paper: 

HARMONIC ANALYSIS ON THE PROPER VELOCITY GYROGROUP

 
 
Author(s):  FERREIRA MILTON*
 
* 
 
Abstract: 

In this article we study harmonic analysis on the proper velocity (PV) gyrogroup using the gyrolanguage of analytic hyperbolic geometry. This 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 zz and on the radius tt of the hyperboloid, and it 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 and its inverse, and Plancherel’s theorem. In the limit of large tt, t?+¥, the generalized harmonic analysis on the hyperboloid tends to the standard Euclidean harmonic analysis on RnRn, thus unifying hyperbolic and Euclidean harmonic analysis.

 
Keyword(s): PV GYROGROUP, LAPLACE-BELTRAMI OPERATOR, EIGENFUNCTIONS, GENERALIZED HELGASON–FOURIER TRANSFORM, PLANCHEREL’S THEOREM
 
 
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APA: Copy

FERREIRA, M. (2017). HARMONIC ANALYSIS ON THE PROPER VELOCITY GYROGROUP. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 11(1), 21-49. https://www.sid.ir/en/journal/ViewPaper.aspx?id=573148



Vancouver: Copy

FERREIRA MILTON. HARMONIC ANALYSIS ON THE PROPER VELOCITY GYROGROUP. BANACH JOURNAL OF MATHEMATICAL ANALYSIS. 2017 [cited 2021July27];11(1):21-49. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=573148



IEEE: Copy

FERREIRA, M., 2017. HARMONIC ANALYSIS ON THE PROPER VELOCITY GYROGROUP. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, [online] 11(1), pp.21-49. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=573148.



 
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