In this talk I will discuss Strichartz estimates on the Heisenberg group for the linear Schrödinger and wave equations involving the sublaplacian. The Schrödinger equation on the Heisenberg group is an example of a totally non-dispersive evolution equation: for this reason the classical approach that permits to obtain Strichartz estimates from dispersive estimates is not available.

Our approach, inspired by the Fourier transform restriction method initiated by Tomas and Stein, is based on Fourier restriction theorems, using the non-commutative Fourier transform on the Heisenberg group. It enables us to obtain also an anisotropic Strichartz estimate for the wave equation, for a larger range of indices than was previously known.