图上分段中心对称Jacobi算子的谱抽取
Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs
摘要：
研究了一类定义在相关的置换图族上的分段中心对称Jacobi算子的谱理论。给定有限有向路图上的有限中心对称矩阵作为权矩阵，局部有限强连通图上的概率拉普拉斯算子作为权矩阵，通过边替换构造了一个新的图和一个新的算子.我们的主要结果证明了利用某些正交多项式，分段中心对称Jacobi算子的谱理论可以与概率Laplacian算子的谱理论明确地联系起来.我们的主要工具涉及所谓的光谱抽取，已知从分形分析，和经典的舒尔补。我们包括几个例子的自相似雅可比矩阵，适合我们的框架。
英文摘要：
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix viewed as a weight matrix on a finite directed path graph and a probabilistic Laplacian viewed as a weight matrix on a locally finite strongly connected graph, we construct a new graph and a new operator by edge substitution. Our main result proves that the spectral theory of the piecewise centrosymmetric Jacobi operator can be explicitly related to the spectral theory of the probabilistic Laplacian using certain orthogonal polynomials. Our main tools involve the so-called spectral decimation, known from the analysis on fractals, and the classical Schur complement. We include several examples of self-similar Jacobi matrices that fit into our framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
