Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010Spectral problems. Issue dedicated to the memory of M. Birman
|Page(s)||198 - 224|
|Published online||12 May 2010|
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
Mathematisches Institut, Friedrich Schiller Universität Jena
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 47B39 / 60J27
Key words: Dirichlet forms / graphs, essential self adjointness / essential spectrum / isoperimetric inequalities / stochastic completeness
© EDP Sciences, 2010
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