Estimates on the number of scattering poles near the real axis for strictly convex obstacles. (English) Zbl 0784.35073

For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus \(\leq r\) in a small angle \(\theta\) near the real axis, can be estimated by Const. \(\theta^{3/2}r^ n\) for \(r\) sufficiently large depending on \(\theta\). Here \(n\) is the dimension.


35P20 Asymptotic distributions of eigenvalues in context of PDEs
35S15 Boundary value problems for PDEs with pseudodifferential operators
35P25 Scattering theory for PDEs
47A20 Dilations, extensions, compressions of linear operators
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