Abstract
Introduction. In the preceding paper [8] we proved that if all harmonic functions in n-dimensional bounded domain D satisfy the mean value property (MVP) with respect to some point P and a given density function ,t (volumedensity, surface-density, etc.) then, under some simple assumptions on ,, 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 ,u (u>?0) under which the MVP holds at most for a finite number of linearly independent functions. The MVP is meant to be:
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