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The Jacobi-Dunkl transform on ℝ and the convolution product on new spaces of distributions

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Abstract

In this work, we consider the Jacobi-Dunkl operator Λα,β, \(\alpha\geq\beta\geq\frac{-1}{2}\) , \(\alpha\neq\frac{-1}{2}\) , on ℝ. The eigenfunction \(\Psi_{\lambda}^{\alpha,\beta}\) of this operator permits to define the Jacobi-Dunkl transform. The main idea in this paper is to introduce and study the Jacobi-Dunkl transform and the Jacobi-Dunkl convolution product on new spaces of distributions

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Gabès University, Gabès, Tunisia

    Hassen Ben Mohamed

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  1. Hassen Ben Mohamed
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Correspondence to Hassen Ben Mohamed.

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Ben Mohamed, H. The Jacobi-Dunkl transform on ℝ and the convolution product on new spaces of distributions. Ramanujan J 21, 145–171 (2010). https://doi.org/10.1007/s11139-009-9171-3

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  • DOI: https://doi.org/10.1007/s11139-009-9171-3

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