Heat traces and existence of scattering resonances for bounded   potentials
  We show that, in odd dimensions, any real valued, bounded potential of compact support has at least one scattering resonance. For dimensions three and higher this was previously known only for sufficiently smooth potentials. The proof is based on an inverse result, which states that the trace of the associated heat kernel has an appropriate asymptotic expansion if and only if the potential is smooth. 
Hart F. Smith and Maciej Zworski
math.AP