Phase space localization of Riesz bases

We discuss uncertainty principle for Riesz bases generated by time frequency shifts of a sequence of functions. Such sequences can not be well localized in the phase space, the optimal localization is achieved by an orthonormal basis constructed by Bourgain. The main tools we use are standard non-commutativity relations and localization operators. As a corollary we show that there are no sampling and interpolating sequences in the Bargam-Fock space in several dimensions. The talk is based on on a joint work with K. Gröchenig.