论文标题
部分可观测时空混沌系统的无模型预测
Semiclassical analysis of a nonlocal boundary value problem related to magnitude
论文作者
论文摘要
我们研究了与歧管中的分数拉普拉斯相关的差异边界问题。它的变异配方是在大小的研究中出现的，该研究是由基态能量给出的紧凑型公制空间的不变。使用针对假数分化边界问题开发的最新技术，我们讨论了解决方案操作员的结构以及幅度的产生特性。在半经典限制中，我们从歧管和边界的曲率不变性方面获得了大小的渐近膨胀，类似于在热核的短时膨胀中产生的不变性。
We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using recent techniques developed for pseudodifferential boundary problems we discuss the structure of the solution operator and resulting properties of the magnitude. In a semiclassical limit we obtain an asymptotic expansion of the magnitude in terms of curvature invariants of the manifold and the boundary, similar to the invariants arising in short-time expansions for heat kernels.
