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

Published online by Cambridge University Press:  12 May 2010

M. Keller  and
D. Lenz
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Abstract

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.

Keywords

Dirichlet formsgraphs, essential self adjointnessessential spectrumisoperimetric inequalitiesstochastic completeness
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 198 - 224
Copyright
© EDP Sciences, 2010

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