The simple definition of a mean is that of a numeric quantity which represents the center of a collection of numbers. Here the trick lies in defining the exact type of numeric collection, as beyond ...
In this note we show that if the areal mean-value theorem holds for a plane domain (subject to a mild regularity condition) for all integrable harmonic functions, then the domain must be a disk. It is ...
https://doi.org/10.4169/amer.math.monthly.124.6.535 https://www.jstor.org/stable/10.4169/amer.math.monthly.124.6.535 We investigate functions with the property that ...
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