Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets

We prove a Calder\'on reproducing formula for the Dunkl continuous wavelet transform on $\mathbb{R}$. We apply this result to derive new inversion formulas for the dual Dunkl-Sonine integral transform

Taylor series associated with a differential-difference operator on the real line

AbstractWe extend the classical theory of Taylor series to a first-order differential-difference operator Λ on the real line which includes as a particular case the Dunkl operator associated with the reflection group Z2 on R. More precisely, we establish first a generalized Taylor formula with integral remainder, and then specify sufficient conditions for a function on R to be expanded as a generalized Taylor series. Moreover, we provide a criterion of analyticity for functions on R involving the differential-difference operator Λ

Hardy and Cowling-Price theorems for a Cherednik type operator on the real line

summary:This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line