标题： 离散图上拉普拉斯算子的谱比较结果 显示英文标题

标题： Spectral comparison results for Laplacians on discrete graphs

摘要： 在最近的文献中，许多作者研究了不同设置下的Schrödinger算子的谱比较结果，包括欧几里得区域和量子图。 在本文中，我们在一个相当一般的框架下推导出一般且可能无限的离散图的此类谱比较结果。 在此过程中，我们建立了一个离散版本的局部Weyl定律，其证明既不涉及任何Tauberian定理，也不涉及连续情况下使用的Weyl定律。 显示英文摘要

摘要： In the recent literature, various authors have studied spectral comparison results for Schr\"odinger operators with discrete spectrum in different settings including Euclidean domains and quantum graphs. In this note we derive such spectral comparison results in a rather general framework for general and possibly infinite discrete graphs. Along the way, we establish a discrete version of the local Weyl law whose proof does neither involve any Tauberian theorem nor the Weyl law as used in the continuous case.