Bogdanova, I.
Vandergheynst, P.
Gazeau, J.
Wavelets on the 2-Hyperboloid
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.
Fourier-Helgason transform;
LTS2;
non-commutative harmonic analysis;
wavelets;
Ecublens
2004
http://infoscience.epfl.ch/record/87065/files/Bogdanova2004_1162.pdf;