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Zbl 1033.42032
Fabec, R.; Ólafsson, G.
The continuous wavelet transform and symmetric spaces.
(English)
[J] Acta Appl. Math. 77, No. 1, 41-69 (2003). ISSN 0167-8019; ISSN 1572-9036/e

It is well known that the wavelet transform is related to a representation of the $ax+b$ group. The present paper concerns generalizations via a representation of a closed subgroup $H$ of $GL(n,\bbfR)$ on $\bbfR^n$. Under certain conditions such a representation leads to a decomposition of $L^2(\bbfR^n)$ into a finite number of irreducible representations, $L^2(\bbfR^n)= V_1 \oplus V_2 \oplus \cdots \oplus V_k$ (via the action of the semidirect product $H\times_s \bbfR^n$). The article focusses on the case where the stabilizer of a generic point in $\bbfR^n$ is a symmetric noncompact subgroup. In particular, it is proved that the generalized wavelet transform is invertible in this case.
[Ole Christensen (Lyngby)]
MSC 2000:
*42C40 Wavelets
43A85 Analysis on homogeneous spaces
22E30 Analysis on real and complex Lie groups

Keywords: wavelet transform

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