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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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