Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We
focus on phenomena related to unboundedness of the Laplacians. This includes
(failure of) essential selfadjointness, absence of essential spectrum and
stochastic incompleteness.

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