一类耗散扰动的谱包含与谱污染
Spectral Inclusion and Pollution for a Class of Dissipative Perturbations
摘要：
证明了希尔伯特空间上$T_0 + i γs_n$形式的线性算子序列的谱包含和谱污染结果，其中$s_n$强收敛于恒等算子和$γ> 0$ .我们的工作在一个抽象的设置和一个更具体的Sturm-Liouville框架。这些结果为计算谱隙中本征值的方法提供了严格的依据。
英文摘要：
Spectral inclusion and spectral pollution results are proved for sequences of linear operators of the form $T_0 + i γs_n$ on a Hilbert space, where $s_n$ is strongly convergent to the identity operator and $γ> 0$. We work in both an abstract setting and a more concrete Sturm-Liouville framework. The results provide rigorous justification for a method of computing eigenvalues in spectral gaps.
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