论文标题
Schrödinger操作员在Flat Tori上的所有特征值的光谱渐近学
Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori
论文作者
论文摘要
我们研究具有浮雕边界条件的Schrödinger操作员在扁平托里上获得光谱结果，从而使所有特征值的渐近膨胀。对于大多数特征值$λ$（稳定的特征值）而言，扩展为$λ^{ - δ} $，$δ\ in（0,1）$，而其余的特征值（不稳定的特征值）是“定向扩展”。证明基于一个结构定理，该定理是\ cite {ps10，ps12}和新的迭代quasimode参数证明的变体。
We study Schrödinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in $λ^{-δ}$ with $δ\in(0,1)$ for most of the eigenvalues $λ$ (stable eigenvalues), while it is a "directional expansion" for the remaining eigenvalues (unstable eigenvalues). The proof is based on a structure theorem which is a variant of the one proved in \cite{PS10,PS12} and on a new iterative quasimode argument.
