Functional Analysis
On the structure of the space of wavelet transforms
Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 649-652.

Let G be the “ax+b”-group with the left invariant Haar measure dν and ψ be a fixed real-valued admissible wavelet on L2(R). The complete decomposition of L2(G,dν) onto the space of wavelet transforms Wψ(L2(R)) is obtained after identifying the group G with the upper half-plane Π in C.

Soient G le groupe affine « ax+b », dν une mesure de Haar invariante à gauche sur G et ψ une ondelette réelle admissible dans L2(R). La décomposition complète de L2(G,dν) sur les espaces des transformées en ondelette Wψ(L2(R)) est obtenue, par l'identification du groupe G avec le demi-plan supérieur Π dans C.

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DOI: 10.1016/j.crma.2008.04.013
Hutník, Ondrej 1

1 Institute of Mathematics, Faculty of Science, P.J. Šafárik University in Košice, Jesenná 5, 04154 Košice, Slovakia
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Hutník, Ondrej. On the structure of the space of wavelet transforms. Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 649-652. doi : 10.1016/j.crma.2008.04.013. http://www.numdam.org/articles/10.1016/j.crma.2008.04.013/

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