Sharp polynomial bounds on the number of scattering poles of radial potentials

AbstractIt is shown that for scattering by a radially symmetric potential in RN, N odd, the number of poles in a disk of radius r satisfies an estimate n(r) ⩽ CN(r + 1)N. This bound is sharp as shown by the special case of potentials nonvanishing at the boundary, where n(r) = KNaNrN(1 + o(1)), a being the diameter of the support