Abstract
We extend Hardy's theorem for rotation due to Lakey and Hogan for Dunkl transform associated with the reflection group in by using Dunkl-Hermite semigroup. In fact, we characterize by considering the decay of f and it's Dunkl transform along some lines in the complex plane, and we give a d-dimensional analogue for the same corresponding to the reflection group Moreover, we prove a version of Hardy's theorem, assuming the decay of Dunkl-Hermite coefficients.
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