Strichartz Estimates for the Schrödinger Equation with a Measure-Valued Potential

Abstract

We prove Strichartz estimates for the Schrödinger equation in ${\mathbb{R}}^n$, $n\ge 3$, with a Hamiltonian $H=-\Delta +\mu$. The perturbation $\mu$ is a compactly supported measure in ${\mathbb{R}}^n$ with dimension $\alpha >n-(1+\frac{1}{n-1})$. The main intermediate step is a local decay estimate in $L^2(\mu )$ for both the free and perturbed Schrödinger evolution.

16 pages, submitted