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Applied and Computational Harmonic Analysis 23 (2007) 285-306
Continuous Wavelet Transform on the Hyperboloid
I. Bogdanova, P. Vandergheynst, J.-P. Gazeau1

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 ptojection. 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.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
Mathématiques/Physique mathématique

Physique/Physique mathématique
non-commutative harmonic analysis – wawelets – Fourier-Helgason transform
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