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Abstract So far, the uncertainty principles for solvable non-exponential Lie groups have been treated only in few cases. The first author and Kaniuth produced an analogue of Hardy's theorem for a diamond Lie group, which is a semi-direct product of ℝ d with the Heisenberg group ℍ 2 d + 1 ${\mathbb {H}_{2d+1}}$ In this setting, we formulate and prove in this paper some other uncertainty principles (Miyachi, Cowling–Price and L p - L q Morgan). This allows us to provide a refined version of Hardy's theorem and to study the sharpness problems.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Oct 1, 2015
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