Geodesic
The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 729-736

Voir la notice de l'article provenant de la source Cambridge University Press

In this work we introduce a class of discrete groups containing subgroups of abstract translations and dilations, respectively. A variety of wavelet systems can appear as $\pi \left( \Gamma\right)\psi $ , where $\pi $ is a unitary representation of a wavelet group and $\Gamma $ is the abstract pseudo-lattice $\Gamma $ . We prove a sufficent condition in order that a Parseval frame $\pi \left( \Gamma\right)\psi $ can be dilated to an orthonormal basis of the form $\tau \left( \Gamma\right)\Psi $ , where $\tau $ is a super-representation of $\pi $ . For a subclass of groups that includes the case where the translation subgroup is Heisenberg, we show that this condition always holds, and we cite familiar examples as applications.
DOI : 10.4153/CMB-2013-005-1
Mots-clés : 43A65, 42C40, 42C15, frame, dilation, wavelet, Baumslag-Solitar group, shearlet 
Currey, B.; Mayeli, A. The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 729-736. doi: 10.4153/CMB-2013-005-1
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