Estimates on the number of scattering poles near the real axis for strictly convex obstacles (Q1313321)

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.