Lower bounds on the number of scattering poles. (English) Zbl 0784.35070

The authors provide several examples for which they can give lower bounds on the number of scattering poles inside a ball of radius \(R\), with \(R\) large enough. Their examples include scattering by obstacles, perturbations of the Euclidean metric, and hyperbolic manifolds. In each case, they obtain a lower bound growing polynomially as \(R\) tends to infinity.


35P15 Estimates of eigenvalues in context of PDEs
35P25 Scattering theory for PDEs
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