论文标题
Klaus-Sparse图上离散Laplacian的基本频谱
The Essential Spectrum of the Discrete Laplacian on Klaus-sparse Graphs
论文作者
论文摘要
1983年，克劳斯（Klaus）研究了一类带有颠簸的电势，并在Infinity的某些定位借助了相关的schr {Ö} Dinger操作员的基本频谱。一个关键的假设是，两个连续颠簸之间的距离倾向于无穷大。在本文中，我们介绍了一个新的图表（带有模拟这种情况的模式），从某种意义上说，两种模式之间的距离倾向于无穷大。这些模式在某种程度上趋向于渐近图。它们是无穷大的地方。我们的结果是，作用于我们图的拉普拉斯的基本频谱是由作用于渐近图的拉普拉斯谱的结合给出的。我们还讨论了附录中基本频谱的稳定性问题。
In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schr{ö}dinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two consecutive bumps tends to infinity at infinity. In this article, we introduce a new class of graphs (with patterns) that mimics this situation, in the sense that the distance between two patterns tends to infinity at infinity. These patterns tend, in some way, to asymptotic graphs. They are the localisations at infinity. Our result is that the essential spectrum of the Laplacian acting on our graph is given by the union of the spectra of the Laplacian acting on the asymptotic graphs. We also discuss the question of the stability of the essential spectrum in the appendix.
