Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: LAMIA JAAFAR BELAID and KHÉLIFA TRIMÈCHE
Pages: [33] - [62]
Received Date: February 8, 2012
Submitted by:
The goal of this work is to generalize the important subject of linear
wavelet packets to the case of harmonic analysis on the Laguerre
generalized hypergroup. For that, we consider the family of Laguerre
functions defined on 
which are eigenfunctions of a given
differential operator. These functions satisfy a product formula,
which permits to define a convolution structure on 
leading to obtain a commutative hypergroup
called the generalized Laguerre hypergroup. Using some harmonic
analysis results on 
we present a construction of a linear
wavelet packets and of the corresponding linear wavelet packet
transform, and we prove for this transform a reconstruction formula.
Finally, using the corresponding scale discrete linear scaling
function, we establish new reconstruction formulas on the Laguerre
generalized hypergroup.
generalized Laguerre hypergroup, harmonic analysis, linear wavelet packet, linear wavelet packet transform, scale discrete linear scaling function.
