Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials

M. Burak Erdogan, Michael Goldberg, William R. Green

We prove a family of dispersive estimates for the higher order Schrödinger equation $i{u}_t=(-\Delta {)}^{m}u+Vu$ for $m\in \mathbb{N}$ with $m>1$ and $2m<n<4m$. Here $V$ is a real-valued pote…