论文标题
超阳性确定功能II：分支机构操作员的完整研究
Hyper-positive definite functions II: A complete study of branching-Toeplitz operators
论文作者
论文摘要
我们介绍并或多或少完整地研究了Hilbert Space $ \ ell^2（T_Q）$由根生均匀的树$ t_q $ t _级$ q \ ge 2 $索引的分支机构运营商$ \ ell^2（T_Q）$。此类操作员的有限维数类似物形成了一个非常自然的结构化稀疏矩阵家族，称为分支toeplitz矩阵，也将进行研究。本文中的分支机构操作员/矩阵应被视为标准Toeplitz操作员/矩阵的天然概括。我们将应用结果来构建一个均匀树木的均匀树木的确定点过程，这些树是分支型强的固定随机过程。
We introduce and give a more or less complete study of a family of branching-Toeplitz operators on the Hilbert space $\ell^2(T_q)$ indexed by a rooted homogeneous tree $T_q$ of degree $q\ge 2$. The finite dimensional analogues of such operators form a very natural family of structured sparse matrices called branching-Toeplitz matrices and will also be investigated. The branching-Toeplitz operators/matrices in this paper should be viewed as natural generalizations of the standard Toeplitz operators/matrices. We will apply our results to construct a family of determinantal point processes on homogeneous trees which are branching-type strong stationary stochastic processes.
