Parametrices and dispersive estimates for Schrödinger operators with variable coefficients

Abstract

In this article we consider variable coefficient time dependent Schr\"odinger evolutions in ${\Bbb R}^n$. Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of $C^2$ metrics which satisfy a weak asymptotic flatness condition at infinity.