Strichartz estimates for the Schrödinger equation with a measure-valued potential

Abstract

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