Bogdanova, I.Vandergheynst, P.Gazeau, J.2006-06-142006-06-142006-06-142004https://infoscience.epfl.ch/handle/20.500.14299/231487We 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 transformLTS2non-commutative harmonic analysiswaveletstext::report