Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
Functional Analysis
2011-01-18 v1 Mathematical Physics
math.MP
Spectral Theory
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.
Cite
@article{arxiv.1101.2979,
title = {Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation},
author = {Matthias Keller and Daniel Lenz},
journal= {arXiv preprint arXiv:1101.2979},
year = {2011}
}