The linear canonical wavelet packet associated with the Dunkl-type operator

In this paper, we introduce the concept of the linear canonical wavelet packet associated with the Dunkl-type operator and establish some of its harmonic analysis properties. More precisely, we consider wavelet packets related to the Dunkl-type operator and study the corresponding wavelet packet transforms. In particular, we introduce the Dunkl-type linear canonical scale discrete scaling function on R, S-wavelet packet, and modified wavelet packet transforms, and for each of these transforms, we establish the reconstruction formula, Parseval's formula, and the Plancherel-type formulas along with those associated with the scale discrete scaling functions.