William R. Green

collaborators

4 papers

math.AP2019

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

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

We prove Strichartz estimates for the Schrödinger equation in $R^{n}$ , $n \geq 3$ , with a Hamiltonian $H = - Δ + μ$ . The perturbation $μ$ is a compactly supported measure in $\m…

math.AP2019

On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances

Burak Erdogan, William R. Green, Ebru Toprak

We study the fourth order Schrödinger operator $H = (- Δ)^{2} + V$ for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and st…

math.AP2018

On the Fourth order Schrödinger equation in four dimensions: dispersive estimates and zero energy resonances

William R. Green, Ebru Toprak

We study the fourth order Schrödinger operator $H = (- Δ)^{2} + V$ for a decaying potential $V$ in four dimensions. In particular, we show that the $t^{- 1}$ decay rate holds in the $L^1\t…

math.AP2018

The Massless Dirac Equation in Two Dimensions: Zero-Energy Obstructions and Dispersive Estimates

Burak Erdogan, Michael Goldberg, William R. Green

We investigate $L^{1} \to L^{\infty}$ dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies th…