Functions Satisfying the Mean Value Property

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1962Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 102, page 167 (issn: 0002-9947,

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Authors: Friedman, Avner; Littman, Walter;

doi: 10.2307/1993885 , 10.1090/s0002-9947-1962-0151628-9

Functions Satisfying the Mean Value Property

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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:

Keywords

partial differential equations

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