Harmonic analysis for graph refinements and the continuous graph FFT
The discrete Fourier transforms (DFT) and their fast algorithms (FFT) are extended to continuous graphs with equal edge lengths. After a review of differential operators on continuous graphs, the spectral theory of standard Laplace differential operators for continuous graphs and their uniformly sampled subgraphs is explored. After these preliminaries, a continuous graph DFT is defined. Fast algorithms for this DFT and its inverse are described. Finally, an example is presented.
scientific article; zbMATH DE number 5561694