Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy

We investigate L(R) → L∞(R4) dispersive estimates for the Schrödinger operator H = −∆ + V when there are obstructions, a resonance or an eigenvalue, at zero energy. In particular, we show that if there is a resonance or an eigenvalue at zero energy then there is a time dependent, finite rank operator Ft satisfying ‖Ft‖L1→L∞ . 1/ log t for t > 2 such that… CONTINUE READING