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 Hilbert space, geometry, boundary constructions, and spectral invariants. focus particular classes graphs, including such weighted graphs which arise electrical network models, as well diagrammatic graph representations. further stress some direct parallels between our one hand, and, other, specific areas potential theory, probability, functions, theory. The limit finite to infinite, local global, can be used various applications.