Sharp upper bounds on the number of the scattering poles

Plamen Stefanov

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Sharp upper bounds on the number of the scattering poles

Plamen Stefanov

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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 $N(r) \le A_n r^n(1+o(1))$ with an explicit constant $A_n$. In a few special cases, we show that this estimate turns into an asymptotic.

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Plamen Stefanov. 2004-12-30. Sharp upper bounds on the number of the scattering poles. https://arxiv.org/abs/math/0412536

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