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We examine an inverse backscattering property of wave motion imposed by anobstacle. We show that if the wave propagator decays super-exponentially alongthe back-scattered geodesics, then the involved scatterer must be trivial. Inparticular, if the fundamental solution decays super-exponentially some timeafter t=0, it vanishes for all time. We use finite speed of propagation in thisarticle.

A Super-Exponential Decaying Property of Odd-Dimensional Wave Scattered by an Obstacle