Coincidence of Harmonic and Finely Harmonic Functions
Article First Online: 27 April 2010 Received: 04 December 2009 Accepted: 12 April 2010 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
This research was supported by Science Foundation Ireland under Grant 09/RFP/MTH2147, and is also part of the programme of the ESF Network “Harmonic and Complex Analysis and Applications” (HCAA).
Armitage, D.H., Gardiner, S.J.: Classical Potential Theory. Springer, London (2001)
MATH Google Scholar
Fugard, T.B.: On the largest ball of harmonic continuation. J. Math. Anal. Appl.
, 548–554 (1982)
MATH CrossRef MathSciNet Google Scholar
Fuglede, B.: Finely Harmonic Functions. Lecture Notes in Math., 289. Springer, Berlin (1972)
Fuglede, B.: Fonctions harmoniques et fonctions finement harmoniques. Ann. Inst. Fourier (Grenoble)
(4), 77–91 (1974)
MATH MathSciNet Google Scholar
Gardiner, S.J.: Sets of harmonicity for finely harmonic functions. Potential Anal.
, 1–6 (2004)
MATH CrossRef MathSciNet Google Scholar Copyright information
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