论文标题
光谱渐近学和节点集中的界面
Interfaces in spectral asymptotics and nodal sets
论文作者
论文摘要
这在很大程度上是对与光谱渐近学的界面共同获得的结果的调查，这既适用于$ l^2（{\ Mathbb r}^d）$的Schrödinger运营商，以及用于holomorphic line line line $ $ $ $ $ $ l l l l f toeplitz hamiltonians conteriant toeplitz hamiltonians cative toeplitz hamiltonians cathertonian ω）$。界面是指在物理空间$ {\ mathbb r}^d $中或相位空间中的超曲面，将光谱渐近性是标准化的允许区域分开，并且是非标准性的禁区。主要的问题是给出整个超曲面（即接口）之间两种类型的渐近药之间的详细过渡。在RealSchrödinger的环境中，渐近型是通风的类型。在Kähler设置中，它们是ERF（高斯错误函数）类型的。此外，我们在该环境中介绍了正遗传线捆绑包和研究界面的Bargmann-Fock空间。
This is largely a survey of results obtained jointly with Boris Hanin and Peng Zhou on interfaces in spectral asymptotics, both for Schrödinger operators on $L^2({\mathbb R}^d)$ and for Toeplitz Hamiltonians acting on holomorphic sections of ample line bundles $L \to M$ over Kähler manifolds $(M, ω)$. By an interface is meant a hypersurface, either in physical space ${\mathbb R}^d$ or in phase space, separating an allowed region where spectral asymptotics are standard and a forbidden region where they are non-standard. The main question is to give the detailed transition between the two types of asymptotics across the hypersurface (i.e. interface). In the real Schrödinger setting, the asymptotics are of Airy type; in the Kähler setting they are of Erf (Gaussian error function) type. In addition, we introduce the Bargmann-Fock space of a positive Hermitian line bundle and study interface asymptotics in that setting.
