论文标题
非亚伯群体作用的逆频谱结果
Inverse spectral results for non-abelian group actions
论文作者
论文摘要
在本文中，我们将扩展到非亚伯群体逆频谱结果，我们在较早的论文中证明了紧凑的阿贝尔群体，即tori。更准确地说，让$ \ mathsf g $是一个紧凑的谎言组，在紧凑的riemannian歧管上iSometimemortion conterains $ x $。我们将证明，对于Schrödingeroperator $ - \ hbar^2δ+v $，$ v \ in c^\ infty（x）^{\ Mathsf g} $，在一些有趣的示例中，潜在函数$ v $由$ \ m m i \ m m i \ m g $ equivariant spectrum确定。此证明中的关键成分是Lagrangian歧管$ \ MATHRM {graph}（dv）$和$ \ mathrm {graph}（df）$之间的广义Legendrian关系，其中$ f $是在阳性Weyl Chamber的开放子集中定义的光谱不变。
In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier paper, for compact abelian groups, i.e. tori. More precisely, Let $\mathsf G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $X$. We will show that for the Schrödinger operator $-\hbar^2 Δ+V$ with $V \in C^\infty(X)^{\mathsf G}$, the potential function $V$ is, in some interesting examples, determined by the $\mathsf G$-equivariant spectrum. The key ingredient in this proof is a generalized Legendrian relation between the Lagrangian manifolds $\mathrm{Graph}(dV)$ and $\mathrm{Graph}(dF)$, where $F$ is a spectral invariant defined on an open subset of the positive Weyl chamber.
