L. A. Bunimovich and B. Z. Webb developed a theory for transforming a finite weighted graph while preserving its spectrum, referred as isospectral reduction theory. In this workwe extend this theory to a class of operators on Banach spaces that include Markov type operators. We apply this theory to infinite countable weighted graphs admitting a finite structural set to calculate the stationary measures of a family of countable Markov chains.

中文翻译：

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无限图中的等谱约简

LA Bunimovich和BZ Webb提出了一种在保留光谱范围的同时变换有限加权图的理论，称为等光谱还原理论。在这项工作中，我们将此理论扩展到Banach空间上的一类算子，其中包括Markov型算子。我们将此理论应用于无限可数加权图，该图允许使用有限结构集来计算可数马尔可夫链族的平稳度量。