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Journal of Spectral Theory

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Volume 10, Issue 3, 2020, pp. 955–989
DOI: 10.4171/JST/318

Published online: 2020-09-16

Isospectral reduction in infinite graphs

Pedro Duarte[1] and Maria Joana Torres[2]

(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