Sharp upper bounds on the number of the scattering poles

Details Sharp upper bounds on the number of the scattering poles Sharp upper bounds on the number of the scattering poles

2004-12-30

arxiv.org/abs/math/0412536v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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