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Sjöstrand, J.; Zworski, M.

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

Ann. Inst. Fourier 43, No. 3, 769-790 (1993).
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.
Reviewer: J.Sjöstrand (Orsay)

Cited in 2 Reviews
Cited in 7 Documents

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

Keywords:

resonance; complex scaling; semiclassical problem; Dirichlet Laplacian; exterior of a strictly convex obstacle; scattering poles
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\textit{J. Sjöstrand} and \textit{M. Zworski}, Ann. Inst. Fourier 43, No. 3, 769--790 (1993; Zbl 0784.35073)
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References:

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