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Generalized Analogs of the Heisenberg Uncertainty Inequality

Abstract

We investigate locally compact topological groups for which a generalized analogue of Heisenberg uncertainty inequality hold. In particular, it is shown that this inequality holds for Rn×K\mathbb{R}^n \times K (where KK is a separable unimodular locally compact group of type I), Euclidean Motion group and several general classes of nilpotent Lie groups which include thread-like nilpotent Lie groups, 22-NPC nilpotent Lie groups and several low-dimensional nilpotent Lie groups

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