HARDY’S THEOREM FOR GABOR TRANSFORM

What is it about?

Hardy’s uncertainty principle for the Gabor transform is proved for locally compact abelian groups having noncompact identity component and groups of the form Rn×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×D , where D is a discrete group.

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