标题： 无限大小平方距离矩阵的谱结构 显示英文标题

标题： Spectral structure of infinite size squared distances matrices

摘要： 在一个度量空间$(X,d)$中选择一个有限点集$\{\xi_1,...,\xi_k\}$，并从它们构造出平方距离矩阵$\mathfrak{D}=(\mathfrak{D}(\xi_i,\xi_j)^2)_{i,j=1}^{k}$。我们提出一种几何方法来研究从黎曼流形$(M,g)$上可数点集$\{\xi_k\}_{k\in \mathbb{Z}}$构造的无限大小平方距离矩阵的谱性质。我们使用行走矩阵从离散问题转移到连续问题。我们描述谱的结构并研究谱流的性质。 显示英文摘要

摘要： Let a finite set of points $\{\xi_1,...,\xi_k\}$ be chosen in a metric space $(X,d)$, and let the squared distance matrix $\mathfrak{D}=(\mathfrak{D}(\xi_i,\xi_j)^2)_{i,j=1}^{k}$ be constructed from them. We propose a geometric approach to studying the spectral properties of squared distance matrices of infinite size, constructed from a countable set of points $\{\xi_k\}_{k\in \mathbb{Z}}$ on Riemannian manifold $(M,g)$. We move from the discrete problem to a continuous one using walk matrices. We describe the structure of the spectrum and study the properties of spectral flows.