Potential Analysis

, Volume 34, Issue 1, pp 81–88

Coincidence of Harmonic and Finely Harmonic Functions



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.


Harmonic function Fine topology Finely harmonic function Baire category 

Mathematics Subject Classification (2010)



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Armitage, D.H., Gardiner, S.J.: Classical Potential Theory. Springer, London (2001)MATHGoogle Scholar
  2. 2.
    Fugard, T.B.: On the largest ball of harmonic continuation. J. Math. Anal. Appl. 90, 548–554 (1982)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fuglede, B.: Finely Harmonic Functions. Lecture Notes in Math., 289. Springer, Berlin (1972)Google Scholar
  4. 4.
    Fuglede, B.: Fonctions harmoniques et fonctions finement harmoniques. Ann. Inst. Fourier (Grenoble) 24(4), 77–91 (1974)MATHMathSciNetGoogle Scholar
  5. 5.
    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

Personalised recommendations