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arXiv · 0707.2346

Hardy's theorem for the q-Bessel Fourier transform

Lazhar Dhaouadi
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Abstract

In this paper we give a q-analogue of the Hardy's theorem for the $q$-Bessel Fourier transform. The celebrated theorem asserts that if a function $f$ and its Fourier transform $\hat{f}$ satisfying $|f(x)|\leq c.e^{-{1/2} x^2}$ and $|\hat{f}(x)|\leq c.e^{-{1/2} x^2}$ for all $x\in\mathbb{% R}$ then $f(x)=\text{const}.e^{-{1/2} x^2}$.

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Lazhar Dhaouadi. 2007-07-16. Hardy's theorem for the q-Bessel Fourier transform. https://arxiv.org/abs/0707.2346

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