The BreitWigner series for noncompactly supported potentials on the line
Abstract
We propose a conjecture stating that for resonances, $\lambda_j$, of a noncompactly supported potential, the series $\sum_j \operatorname{Im} \lambda_j/\lambda_j^2$ diverges. This series appears in the BreitWigner approximation for a compactly supported potential, in which case it converges. We provide heuristic motivation for this conjecture and prove it in several cases.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.13765
 Bibcode:
 2020arXiv200513765B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Complex Variables;
 Mathematics  Spectral Theory;
 35P25
 EPrint:
 10 pages