Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 067, 22 pages      arXiv:0809.5021
Contribution to the Special Issue on Dunkl Operators and Related Topics

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

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

In this paper we prove inversion formulas for the Dunkl intertwining operator Vk and for its dual tVk and we deduce the expression of the representing distributions of the inverse operators Vk−1 and tVk−1, and we give some applications.

Key words: inversion formulas; Dunkl intertwining operator; dual Dunkl intertwining operator.

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