95-443 Lev Kapitanski and Yuri Safarov

Dispersive smoothing for Schr\"odinger equations (39K, AMSTeX) Oct 3, 95

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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 $t=0$.

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