
SIGMA 4 (2008), 067, 22 pages arXiv:0809.5021
http://dx.doi.org/10.3842/SIGMA.2008.067
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
Abstract
In this paper we prove inversion formulas for the Dunkl
intertwining operator V_{k} and for its dual ^{t}V_{k}
and we
deduce the expression of the representing distributions of the
inverse operators V_{k}^{−1} and ^{t}V_{k}^{−1}, and we give some
applications.
Key words:
inversion formulas; Dunkl intertwining operator; dual Dunkl intertwining operator.
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