  We provide a result on the coherent states decomposition for functions in
$L^2 (\Bbb T^n)$ where $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$. Suddenly, we
study such a decomposition with respect to the quantum dynamics related to
semiclassical elliptic Pseudodifferential operators, and we prove a related
invariance result.
