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

DOI

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
@article{10_4153_CMB_2013_005_1,
     author = {Currey, B. and Mayeli, A.},
     title = {The {Orthonormal} {Dilation} {Property} for {Abstract} {Parseval} {Wavelet} {Frames}},
     journal = {Canadian mathematical bulletin},
     pages = {729--736},
     year = {2013},
     volume = {56},
     number = {4},
     doi = {10.4153/CMB-2013-005-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-005-1/}
}
TY  - JOUR
AU  - Currey, B.
AU  - Mayeli, A.
TI  - The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 729
EP  - 736
VL  - 56
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-005-1/
DO  - 10.4153/CMB-2013-005-1
ID  - 10_4153_CMB_2013_005_1
ER  - 
%0 Journal Article
%A Currey, B.
%A Mayeli, A.
%T The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames
%J Canadian mathematical bulletin
%D 2013
%P 729-736
%V 56
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-005-1/
%R 10.4153/CMB-2013-005-1
%F 10_4153_CMB_2013_005_1

Cité par Sources :