Research on spectral structure of dissipative operators and super composition of dissipative systems

我们主要对物理和工程中出现的弱耗散(摩擦)效应的波传播问题进行了数学研究。这项研究是通过使用这种现象的特征频率来完成的，这种频率被称为频谱。我们得到了以下主要结果。对于弱耗散介质中声波的传播，我们决定了波的谱结构和随时间推移的行为。对于电子进入原子时的反射现象，也得到了类似的结果。我们还确定了在远距离观测半空间弹性波(如地震波)时的波的形状。

We mainly did a mathematical research on the wave propagation problem with a weak dissipative (frictional) effect of appearing to physics and engineering. The research was done by using a characteristic frequency of the phenomenon that is called a spectrum. We obtained the following as main results. Concerning acoustic wave propagation in media of weak dissipative effect, we decided the spectral structure and the behavior of waves of the passage of time. Similar results were obtained concerning the reflection phenomenon when electron is entered into atom. We also decided the shape of waves when elastic waves of a half space (for example, seismic waves) is observed at far.