## Lower bounds on the number of scattering poles. II.(English)Zbl 0823.35137

In continuation of their paper [Commun. Partial Differ. Equ. 18, No. 5-6, 847-857 (1993; Zbl 0784.35070)] (where several examples were treated), here the authors obtain a very general lower bound on the number of scattering poles, for a wide class of abstract compactly supported perturbations of the Laplacian in $$\mathbb{R}^ n$$ ($$n$$ odd). The proof is based on the exploitation of the singularities of the wave trace at zero.

### MSC:

 35P25 Scattering theory for PDEs 35P15 Estimates of eigenvalues in context of PDEs 47A40 Scattering theory of linear operators

### Keywords:

resonances; scattering poles

Zbl 0784.35070
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