1 research outputs found
Dispersive estimates for four dimensional Schr\"{o}dinger and wave equations with obstructions at zero energy
We investigate dispersive
estimates for the Schr\"odinger operator 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 satisfying for such that
We also show that the operator if there is an eigenvalue but no
resonance at zero energy. We then develop analogous dispersive estimates for
the solution operator to the four dimensional wave equation with potential.Comment: 32 page