论文标题
从刺耳的不平等到阻尼波方程的光谱围墙
From Lieb-Thirring inequalities to spectral enclosures for the damped wave equation
论文作者
论文摘要
使用阻尼波方程的光谱与非辅助Adchoint Schroedinger操作员之间的对应关系，我们在前者的复杂特征值上得出了各种界限。特别是，我们确定了一个敏锐的结果，即一维阻尼波算子类似于未阻尼的波动，前提是（可能是复杂值）阻尼的L^1规范小于2。因此，这些小型阻尼是无法检测到的。
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.
