Sharp upper bounds on the number of the scattering poles
Plamen Stefanov
Abstract
For various compactly supported perturbations of the Laplacian in odd dimensions n, we prove a sharp upper bound of the resonance counting function N(r) of the type N(r) An rn(1+o(1)) with an explicit constant An. In a few special cases, we show that this estimate turns into an asymptotic.
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