In this work, we consider the Jacobi-Dunkl operator α,β , α ≥ β ≥ −1 2 , α = −1 2 , on R. The eigenfunction α,β λ of this operator permits to define the JacobiDunkl transform. The main idea in this paper is to introduce and study the JacobiDunkl transform and the Jacobi-Dunkl convolution product on new spaces of distributions
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