HAL : in2p3-00025329, version 1

DOI : 10.1016/j.acha.2007.01.003

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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

(2007)

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 - AstroParticule et Cosmologie

équipe(s) de recherche : APC - THEORIE

Thème(s)

:

Mathématiques/Physique mathématique Physique/Physique mathématique

Mot(s)-clé(s) : non-commutative harmonic analysis – wawelets – Fourier-Helgason transform

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Soumis le : Lundi 9 Janvier 2006, 12:19:23

Dernière modification le : Lundi 18 Juin 2012, 14:56:04