Using a correspondence between the spectrum of the damped wave equation and non-self-adjoint Schroedinger operators, we derive various bounds on complex eigenvalues of the former. In particular, we establish a sharp result that the one-dimensional damped wave operator is similar to the undamped one provided that the L^1 norm of the (possibly complex-valued) damping is less than 2. It follows that these small dampings are spectrally undetectable.

中文翻译：

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从 Lieb-Thirring 不等式到阻尼波动方程的谱包络

使用阻尼波动方程谱与非自伴随薛定谔算子之间的对应关系，我们推导出前者复特征值的各种界限。特别是，我们建立了一个尖锐的结果，即一维阻尼波算子类似于无阻尼波算子，前提是（可能是复值）阻尼的 L^1 范数小于 2。因此，这些小阻尼是光谱检测不到。