Lev Kapitanski and Yuri Safarov
Dispersive smoothing for Schr\"odinger equations
(39K, AMSTeX)
ABSTRACT. We study the regularity of the fundamental solution
(Green's function, propagator) for the initial or
initial boundary value problem for the Schr\"odinger
equation (or system) with variable coefficients.
Under certain assumptions, the most essential of
which is the appropriate non-trapping condition,
we prove that the only singularity of the fundamental
solution is at $t=0$.