On the structure of the space of wavelet transforms

Ondrej Hutník

doi:10.1016/j.crma.2008.04.013

Functional Analysis

On the structure of the space of wavelet transforms

Yves Meyer

Ondrej Hutník ¹

¹Institute of Mathematics, Faculty of Science, P.J. Šafárik University in Košice, Jesenná 5, 04154 Košice, Slovakia

Comptes Rendus. Mathématique, Volume 346 (2008) no. 11-12, pp. 649-652

Abstract (Original language)
Résumé

Let G be the “ $a x + b$ ”-group with the left invariant Haar measure dν and ψ be a fixed real-valued admissible wavelet on $L_{2} (R)$ . The complete decomposition of $L_{2} (G, d ν)$ onto the space of wavelet transforms $W_{ψ} (L_{2} (R))$ is obtained after identifying the group G with the upper half-plane Π in $C$ .

Soient G le groupe affine « $a x + b$ », dν une mesure de Haar invariante à gauche sur G et ψ une ondelette réelle admissible dans $L_{2} (R)$ . La décomposition complète de $L_{2} (G, d ν)$ sur les espaces des transformées en ondelette $W_{ψ} (L_{2} (R))$ est obtenue, par l'identification du groupe G avec le demi-plan supérieur Π dans $C$ .

Article information
Cite this article

Received: 2007-07-31
Accepted: 2008-04-23
Published online: 2008-05-20

DOI: 10.1016/j.crma.2008.04.013

Author's affiliations:

Ondrej Hutník ¹

¹ Institute of Mathematics, Faculty of Science, P.J. Šafárik University in Košice, Jesenná 5, 04154 Košice, Slovakia

Ondrej Hutník. 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

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