The logarithmic Laplacian on weighted graphs is defined via a Bochner integral, given a kernel formula under stochastic completeness, and shown on Z^d to have sharp kernel bounds and exact diffusion asymptotics.
Extension problem and harnack’s inequality for some fractional operators
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The Logarithmic Laplacian on General Graphs
The logarithmic Laplacian on weighted graphs is defined via a Bochner integral, given a kernel formula under stochastic completeness, and shown on Z^d to have sharp kernel bounds and exact diffusion asymptotics.