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

M. Keller¹ ; D. Lenz¹

¹ Mathematisches Institut, Friedrich Schiller Universität Jena D-07743 Jena, Germany

Mathematical modelling of natural phenomena, Tome 5 (2010) no. 4, pp. 198-224.

Résumé

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.

Détail

DOI : 10.1051/mmnp/20105409

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