Hardy's theorem for the q-Bessel Fourier transform

Details Hardy's theorem for the q-Bessel Fourier transform Hardy's theorem for the q-Bessel Fourier transform

2007-07-16

arxiv.org/abs/0707.2346v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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