Khalifa Trimèche, “Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions”, SIGMA, 2008, Volume 4,067, 22 pp.

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Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

Khalifa Trimèche

Faculty of Sciences of Tunis, Department of Mathematics, 1060 Tunis, Tunisia

Abstract: In this paper we prove inversion formulas for the Dunkl intertwining operator $V_k$ and for its dual ${}^tV_k$ and we deduce the expression of the representing distributions of the inverse operators $V^{-1}_k$ and ${}^tV_k^{-1}$, and we give some applications.

Keywords: inversion formulas; Dunkl intertwining operator; dual Dunkl intertwining operator.

MSC: 33C80; 43A32; 44A35; 51F15

Received: May 13, 2008; in final form September 16, 2008; Published online September 29, 2008

Language: English

DOI: 10.3842/SIGMA.2008.067