论文标题
在光谱间隙中的最小原理
On a minimax principle in spectral gaps
论文作者
论文摘要
Griesemer，Lewis和Siedentop在[Doc。数学。 4（1999），275--283]适应以涵盖某些抽象扰动设置，具有有限或无限的扰动，尤其是相对于所考虑的频谱差距，尤其是偏离障碍的扰动。这部分是基于作者附录中的注意事项的，并将其扩展到[J.频谱。理论10（2020），843--885]。推导了本特征值在本质频谱间隙中特征值的几种单调性和连续性特性，并以stokes运算符为例。
The minimax principle for eigenvalues in gaps of the essential spectrum in the form presented by Griesemer, Lewis, and Siedentop in [Doc. Math. 4 (1999), 275--283] is adapted to cover certain abstract perturbative settings with bounded or unbounded perturbations, in particular ones that are off-diagonal with respect to the spectral gap under consideration. This in part builds upon and extends the considerations in the author's appendix to [J. Spectr. Theory 10 (2020), 843--885]. Several monotonicity and continuity properties of eigenvalues in gaps of the essential spectrum are deduced, and the Stokes operator is revisited as an example.
