  This paper is dedicated to the proof of Strichartz estimates on the
Heisenberg group $\mathbb{H}^d$ for the linear Schr\"odinger and wave equations
involving the sublaplacian. The Schr\"odinger equation on $\mathbb{H}^d$ 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 on $\mathbb{H}^d$, 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.
