The Galerkin Method for Perturbed Self-Adjoint Operators and Applications
The Galerkin Method for Perturbed Self-Adjoint Operators and Applications
复制标题
扰动自伴算子的伽辽金方法及其应用
DOI：
10.4171/jst/64
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Michael Strauß
中科院分区：
文献类型：
--
作者：
Michael Strauß
考虑了逼近算子$T+ $A的谱的Galerkin方法，其中$T$是半有界自伴随，且$A$满足一个相对紧性条件。我们证明了该方法在所有区域都是可靠的，其中对于非扰动问题（总是包含$\mathbb{C}\反斜杠\mathbb{R}$）是可靠的。结果导致了一种新的技术来识别$T$的特征值，以及识别由直接应用伽辽金方法对$T$产生的光谱污染。新技术的优点在于它适用于表单领域。
We consider the Galerkin method for approximating the spectrum of an operator $T+A$ where $T$ is semi-bounded self-adjoint and $A$ satisfies a relative compactness condition. We show that the method is reliable in all regions where it is reliable for the unperturbed problem - which always contains $\mathbb{C}\backslash\mathbb{R}$. The results lead to a new technique for identifying eigenvalues of $T$, and for identifying spectral pollution which arises from applying the Galerkin method directly to $T$. The new technique benefits from being applicable on the form domain.