Sharp bounds on the number of scattering poles for perturbations of the Laplacian.(English)Zbl 0766.35032

Author’s summary: Sharp bounds on the number $$N(r)$$ of the scattering poles in the disc $$| z|\leq r$$ for large class of compactly supported perturbations (not necessarily selfadjoint) of the Laplacian in $$\mathbb{R}^ n$$, $$n\geq 3$$, odd, are obtained. In particular, in the elliptic case the estimate $$N(r)\leq Cr^ n+C$$ is proved.

MSC:

 35P25 Scattering theory for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 47A40 Scattering theory of linear operators
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References:

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