Unbounded operators and the uncertainty principle

We study a variant of the uncertainty principle in terms of the annihilation and creation operator on generalized Segal Bargmann spaces, which are used for the FBI-Bargmann transform. In addition, we compute the Berezin transform of these operators and indicate how to use spaces of entire functions in one variable to study the Szegő kernel for hypersurfaces in ${\mathbb{C}}^2\mathrm{.}$