Abstract
In (Kaniuth and Kumar in Math. Proc. Camb. Phil. Soc. 131, 487–494, 2001) Hardy’s uncertainty principle for \({\mathbb{R}}^n\) was generalized to connected and simply connected nilpotent Lie groups. In this paper, we extend it further to connected nilpotent Lie groups with non-compact centre. Concerning the converse, we show that Hardy’s theorem fails for a connected nilpotent Lie group G which admits a square integrable irreducible representation and that this condition is necessary if the simply connected covering group of G satisfies the flat orbit condition.
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Baklouti, A., Kaniuth, E. On Hardy’s uncertainty principle for connected nilpotent Lie groups. Math. Z. 259, 233–247 (2008). https://doi.org/10.1007/s00209-007-0219-z
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DOI: https://doi.org/10.1007/s00209-007-0219-z