, Volume 34, Issue 1, pp 81-88
Date: 27 Apr 2010

Coincidence of Harmonic and Finely Harmonic Functions

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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.

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).