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

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 4, page 198-224
- ISSN: 0973-5348

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topKeller, M., and Lenz, D.. "Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation." Mathematical Modelling of Natural Phenomena 5.4 (2010): 198-224. <http://eudml.org/doc/197705>.

@article{Keller2010,

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.},

author = {Keller, M., Lenz, D.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {Dirichlet forms; graphs, essential self adjointness; essential spectrum; isoperimetric inequalities; stochastic completeness; graphs; essential selfadjointness},

language = {eng},

month = {5},

number = {4},

pages = {198-224},

publisher = {EDP Sciences},

title = {Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation},

url = {http://eudml.org/doc/197705},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Keller, M.

AU - Lenz, D.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/5//

PB - EDP Sciences

VL - 5

IS - 4

SP - 198

EP - 224

AB - 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.

LA - eng

KW - Dirichlet forms; graphs, essential self adjointness; essential spectrum; isoperimetric inequalities; stochastic completeness; graphs; essential selfadjointness

UR - http://eudml.org/doc/197705

ER -

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