树上薛定谔算子特征向量零点的交错性
Interlacing Property of Zeros of Eigenvectors of Schrödinger Operators on Trees
摘要：
我们证明了一个类似的树柯朗定理的交错性质的薛定谔算子的本征函数的零点。设$Γ$是有限树，$\mathcal A$是$Γ$上的薛定谔算子.如果$\mathcal A$的特征向量按特征值递增的顺序排列，且零坐标对应的顶点次数至多为2，则特征向量线性扩张的零点具有交错性质.
英文摘要：
We prove an analogue for trees of Courant's theorem on the interlacing property of zeros of eigenfunctions of a Schrödinger operator. Let $Γ$ be a finite tree, and $\mathcal A$ a Schrödinger operator on $Γ$. If the eigenvectors of $\mathcal A$ are ordered according to increasing eigenvalues, and the vertices corresponding to zero coordinates are of degree at most two, then the zeros of the linear extensions of eigenvectors have the interlacing property.
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