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- W1951795495 abstract "We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. We associate to certain subgraphs (domains) a pair of sequences, each of which is invariant under the action of the automorphism group of the underlying graph. We prove that these invariants differ by an explicit combinatorial factor given by Stirling numbers of the first and second kind. We prove that for any domain with a natural weighting, these invariants determine the eigenvalues of the Laplace operator corresponding to eigenvectors with nonzero mean. As a specific example, we investigate the relationship between our invariants and heat content asymptotics, expressing both as special values of an analog of a spectral zeta function." @default.
- W1951795495 created "2016-06-24" @default.
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- W1951795495 date "2002-08-01" @default.
- W1951795495 modified "2023-09-23" @default.
- W1951795495 title "Diffusions on graphs, Poisson problems and spectral geometry" @default.
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- W1951795495 doi "https://doi.org/10.1090/s0002-9947-02-02973-2" @default.
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