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Bezuglyi, Sergey; Jorgensen, Palle E. T.

Harmonic analysis on graphs via Bratteli diagrams and path-space measures. (English) Zbl 1493.37016

Diss. Math. 574, 1-74 (2022).
The paper is devoted to the harmonic analysis of graphs. Specifically, it is focused on those graph systems \(G\) with the property that the sets vertices and edges admit discrete level structures, which was motivated by recent strudies of so-called Bratteli diagrams.
The authors use discrete levels leading to discrete-time random walk models. In this way, they extend the case when the levels in \(G\) are standard measure spaces, comparing to the earlier analysis of Bratelli diagrams.
The paper contains a large number of references on the topic.
Reviewer: Anatoliy Swishchuk (Calgary)

Cited in 1 Review
Cited in 4 Documents

MSC:

37B10 Symbolic dynamics
37A46 Relations between ergodic theory and harmonic analysis
37H10 Generation, random and stochastic difference and differential equations
42B37 Harmonic analysis and PDEs
47L50 Dual spaces of operator algebras
60J45 Probabilistic potential theory
28D05 Measure-preserving transformations

Keywords:

graphs; Bratteli diagrams; electrical networks; graph Laplacian; unbounded operators; Hilbert space; spectral theory; harmonic analysis; dynamical systems; invariant measures; standard measure space; symmetric and path-space measure; Markov operator and process; finite energy space
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Full Text: DOI arXiv

References:

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