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HARDY’S THEOREM FOR GABOR TRANSFORM
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 106 / Issue 2 / April 2019
- Published online by Cambridge University Press:
- 15 August 2018, pp. 143-159
- Print publication:
- April 2019
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- Article
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Hardy’s uncertainty principle for the Gabor transform is proved for locally compact abelian groups having noncompact identity component and groups of the form
$\mathbb{R}^{n}\times K$, where 
$K$ is a compact group having irreducible representations of bounded dimension. We also show that Hardy’s theorem fails for a connected nilpotent Lie group 
$G$ which admits a square integrable irreducible representation. Further, a similar conclusion is made for groups of the form 
$G\times D$, where 
$D$ is a discrete group.
