Harmonic Analysis Invariants for Infinite Graphs Via Operators and Algorithms

We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral invariants. We focus on particular classes of infinite grap...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2021-04, Vol.27 (2), Article 34
Main Authors: Bezuglyi, Sergey, Jorgensen, Palle E. T.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Algorithms
Analysis
Approximations and Expansions
Combinatorial analysis
Electrical networks
Fourier Analysis
Graph representations
Graphical representations
Graphs
Harmonic analysis
Harmonic Analysis on Combinatorial Graphs
Harmonic functions
Hilbert space
Invariants
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial Differential Equations
Potential theory
Signal,Image and Speech Processing
Social networks
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Summary:We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral invariants. We focus on particular classes of infinite graphs, including such weighted graphs which arise in electrical network models, as well as new diagrammatic graph representations. We further stress some direct parallels between our present analysis on infinite graphs, on the one hand, and, on the other, specific areas of potential theory, probability, harmonic functions, and boundary theory. The limit constructions, finite to infinite, and local to global, can be used in various applications.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-021-09827-0