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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Lamplighter graphs do not admit harmonic functions of finite energy


Author: Agelos Georgakopoulos
Journal: Proc. Amer. Math. Soc. 138 (2010), 3057-3061
MSC (2010): Primary 05C25
Published electronically: May 14, 2010
MathSciNet review: 2653930
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Abstract: We prove that a lamplighter graph of a locally finite graph over a finite graph does not admit a non-constant harmonic function of finite Dirichlet energy.


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Additional Information

Agelos Georgakopoulos
Affiliation: Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10279-4
PII: S 0002-9939(2010)10279-4
Received by editor(s): August 12, 2009
Published electronically: May 14, 2010
Additional Notes: The author was supported by FWF grant P-19115-N18
Communicated by: Jim Haglund
Article copyright: © Copyright 2010 Agelos Georgakopoulos