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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.

MSC:

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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References:

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