Wavelet Packets Associated with a Dunkl Type Operator on the Real Line

Abstract

We consider a singular differential-difference operator $\Lambda$ on $\R$ which generalizes the one-dimensional Dunkl operator. Using harmonic analysis associated with $\Lambda$ we define and study three types of generalized wavelet packets and the corresponding wavelet transforms. As an application, we introduce on $\R$ a new multiresolution analysis tied to $\Lambda$.