Analysis on graphs and noncommutative geometry
@article{Davies1993AnalysisOG,
title={Analysis on graphs and noncommutative geometry},
author={E. B. Davies},
journal={Journal of Functional Analysis},
year={1993},
volume={111},
pages={398-430}
}Abstract We study the form of the continuous time heat kernel for a second order discrete Laplacian on a weighted graph. The analysis is shown to be closely related to the theory of symmetric Markov semigroups on noncommutative L p spaces and to the noncommutative geometry of Connes. The paper obtains better pointwise upper bounds on the heat kernels than those previously known, by the use of a novel metric on the graph. In certain cases it is shown that the new estimates are optimal of their…
43 Citations
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