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 $N(r) \le A_n r^n(1+o(1))$ with an explicit constant $A_n$. In a few special cases, we show that this estimate turns into an asymptotic.
Bounds on the number of scattering poles of half-Laplacian in odd dimensions, $d\geq 3$
The $L^p$ boundedness of wave operators for Schrödinger Operators with threshold singularities : Odd dimensions
Scattering Poles Near the Real Axis for Two Strictly Convex Obstacles
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