论文标题
限制sturm-liouville操作员的本征函数，约有光谱流量
Limiting Eigenfunctions of Sturm-Liouville operators Subject to a Spectral Flow
论文作者
论文摘要
我们检查了一个sturm--liouville运算符的频谱，其定期间隔的三角洲功能电位通过增加强度来参数。在该光谱流下特征值的限制行为是在最后两位作者的伯科拉科（Berkolaiko）进行的预期结果中描述的，该作者被用来研究拉普拉斯本征函数的淋巴结缺乏。在这里，我们考虑这些操作员的征征。特别是，我们为限制本征函数提供了明确的公式，并为光谱流参数的所有值（不仅在极限）中表征了所有值的本征函数和特征值。我们还开发了用于比较和可视化的光谱准确的数值工具。
We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a previor result of the last two authors with Berkolaiko, where it was used to study the nodal deficiency of Laplacian eigenfunctions. Here we consider the eigenfunctions of these operators. In particular, we give explicit formulas for the limiting eigenfunctions, and also characterize the eigenfunctions and eigenvalues for all values for the spectral flow parameter (not just in the limit). We also develop spectrally accurate numerical tools for comparison and visualization.
