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We show that, in odd dimensions, any real valued, bounded potential ofcompact support has at least one scattering resonance. For dimensions three andhigher this was previously known only for sufficiently smooth potentials. Theproof is based on an inverse result, which states that the trace of theassociated heat kernel has an appropriate asymptotic expansion if and only ifthe potential is smooth.

Heat traces and existence of scattering resonances for bounded potentials