Metaplectic representation on Wiener amalgam spaces and applications to the Schr\"odinger equation

We study the action of metaplectic operators on Wiener amalgam spaces, giving upper bounds for their norms. As an application, we obtain new fixed-time estimates in these spaces for Schr"odinger equations with general quadratic Hamiltonians and Strichartz estimates for the Schr"odinger equation with potentials $V(x)=\pm \mathrm{\mid }x{\mathrm{\mid }}^2$.