Abstract
In 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 axisymmetric hyperbolic wavelets. The continuous wavelet transform W f ( a , x ) is obtained by convolution of the scaled axisymmetric 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.
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