Hardy's theorem and rotation for Dunkl transform

Sarathi Patra, Partha and Dogga, Venku Naidu (2021) Hardy's theorem and rotation for Dunkl transform. Complex Variables and Elliptic Equations, 66 (1). pp. 71-83. ISSN 1747-6933

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Abstract

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

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