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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