Miyachi’s theorem for oscillator Lie groups

Dhoha Lahyani – GJM, Volume 2, Issue 1 (2017), 1-9.

We formulate and prove an analogue of Miyachi’s theorem for the oscillator groups, which is a semi-direct product of $\mathbb{R}$ with the Heisenberg group $\mathbb{H}_{3}$. This allows us to generalize and prove an analogue of the Hardy and Cowling-Price uncertainty principle on $G$.

Categories: Issue1, 2017