Bogdanova, I.
Vandergheynst, P.
Gazeau, J.
Wavelets on the 2-Hyperboloid
Fourier-Helgason transform
LTS2
non-commutative harmonic analysis
wavelets
2004
2004
We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO_0(1,2)$, we define a family of hyperbolic wavelets. The continuous wavelet transform (CWT)is obtained by convolution of the scaled wavelets with the signal. This wavelet transform is proved to be invertible whenever wavelets satisfy a particular admissibility condition. Finally, the Euclidean limit of this CWT on the hyperboloid is considered.
ITS
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