Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches
Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches
复制标题
非自共轭算子的特征值：两种方法的比较
DOI：
10.1007/978-3-0348-0591-9_2
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
G. Katriel
中科院分区：
文献类型：
--
作者：
M. Demuth;Marcel Hansmann;G. Katriel
我们考虑的中心问题是非自共轭的闭线性算子的特征值分布，重点关注那些作为自共线性算子的扰动而获得的算子。对两种方法进行了解释和阐述。一种方法使用复分析来研究全纯函数，其零点可以用线性算子的特征值来识别。第二种方法是涉及数值范围的算子理论方法。推导并比较了两种方法获得的一般结果。考虑了非自共轭雅可比和薛定谔算子的应用。讨论了未来研究的一些可能的方向。
The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are explained and elaborated. One approach uses complex analysis to study a holomorphic function whose zeros can be identified with the eigenvalues of the linear operator. The second method is an operator theoretic approach involvingthe numerical range. General results obtained by the two methods are derived and compared. Applications to non-selfadjoint Jacobi and Schrodinger operators are considered. Some possible directions for future research are discussed.