A characterization of harmonic functions |
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| Affiliation: | 1. Institute of Mathematics, Physics and Mechanics, E.K. University of Ljubljana, Ljubljana, Yugoslavia;2. Department of Mathematics, University of Wisconsin, Madison, WI 53706, U.S.A. |
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| Abstract: | Gauss' mean value characterization of harmonic functions involves circles (or spheres) centered at every point of the domain of the function. The present paper gives a criterion of this type which involves only one point of the domain; to make up for this, circles or spheres are replaced by a larger family of convex curves or surfaces which surround this point. |
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