We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a semiclassical Schrödinger operator is supposed to be smooth and to decrease at infinity, the usual formulas relating scattering quantities and resonances still hold. The main ingredient for the proofs is a resolvent estimate of a new type, relating the resolvent of an operator with the resolvent of its cut-off counterpart.

中文翻译：

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没有解析性假设的共振理论的应用

我们证明散射理论中涉及共振的结果对于非解析势仍然有效，即使共振的概念在此设置中没有定义。更准确地说，我们表明，如果假设半经典薛定谔算子的势是平滑的并且在无穷远处减小，则有关散射量和共振的常用公式仍然成立。证明的主要成分是新类型的解析度估计，将算子的解析度与其截止对应的解析度相关联。