Potential Analysis

, Volume 34, Issue 1, pp 81–88

Coincidence of Harmonic and Finely Harmonic Functions

Article
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Abstract

This paper answers an old question of Fuglede by characterising those finely open sets U with the following property: any finely harmonic function on U must coincide with a harmonic function on some non-empty finely open subset.

Keywords

Harmonic function Fine topology Finely harmonic function Baire category 

Mathematics Subject Classification (2010)

31C40 

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References

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    Fuglede, B.: Fonctions harmoniques et fonctions finement harmoniques. Ann. Inst. Fourier (Grenoble) 24(4), 77–91 (1974)MATHMathSciNetGoogle Scholar
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    Gardiner, S.J.: Sets of harmonicity for finely harmonic functions. Potential Anal. 21, 1–6 (2004)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College DublinDublin 4Ireland

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