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

Commun. Math. Anal.
Volume 12, Number 1 (2012), 96 - 116

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

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Abstract

We consider a singular differential-difference operator Λ on R which generalizes the one-dimensional Dunkl operator. Using harmonic analysis associated with Λ 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 Λ.