Functions satsifying the mean value property
Avner Friedman, Walter Littman · Transactions of the American Mathematical Society · 1962
Introduction.In the preceding paper [8] we proved that if all harmonic functions in «-dimensional bounded domain D satisfy the mean value property (MVP) with respect to some point P and a given density function p (volumedensity, surface-density, etc.) then, under some simple assumptions on p, D must necessarily be a ball with center P. In the present paper we are interested in studying the MVP from a complementary point of view, namely, we are interested in finding conditions on p (p^O) under which the MVP holds at most for a finite number of linearly independent functions.The