Journal of Spectral Theory
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Published online: 2020-09-16
Isospectral reduction in infinite graphsPedro Duarte and Maria Joana Torres (1) Universidade de Lisboa, Portugal
(2) Universidade do Minho, Braga, Portugal
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.
Keywords: Isospectral graph reduction, Markov operator, eigenvalue problem
Duarte Pedro, Torres Maria Joana: Isospectral reduction in infinite graphs. J. Spectr. Theory 10 (2020), 955-989. doi: 10.4171/JST/318