Lower bounds for the number of resonances in even dimensional potential scattering. (English) Zbl 0939.35133
Let \(V \in {\mathbb C}_0^\infty({\mathbb R}^n,{\mathbb R})\), \(n \geq 4,\) be even, \(P=-\Delta+V\) and \(\{\lambda_j \}\) are resonances of P with multiplicity \(M(\lambda_j)\). It is proved that
\[
\sum_j {M(\lambda_j) \over {|\log|\lambda_j|+i \arg\lambda_j |} } = \infty.
\]
As a direct consequence of this result a lower bound for the number of resonances is obtained.
Reviewer: M.Perelmuter (Kyïv)
MSC:
| 35P25 | Scattering theory for PDEs |
| 47A40 | Scattering theory of linear operators |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
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