Bogdanova, I.Vandergheynst, P.Gazeau, J.2006-06-142006-06-142006-06-14200710.1016/j.acha.2007.01.003https://infoscience.epfl.ch/handle/20.500.14299/231688WOS:00025135320000111714In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid $H_+^2$. First, we define a class of suitable 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 $W_f(a,x)$ is obtained by convolution of the scaled wavelets with the signal. The wavelet transform is proved to be invertible whenever wavelets satisfy a particular admissibility condition, which turns out to be a zero-mean condition. We then provide some basic examples and discuss the limit at null curvature.non-commutative harmonic analysiswaveletsLTS2lts2text::journal::journal article::research article