Inverse Mean Value Property of Metaharmonic Functions

摘要

A new analytical characterization of balls in the Euclidean space ?m is obtained. Previous results of this kind involved either harmonic functions or solutions to the modified Helmholtz equation (both have positive fundamental solutions), whereas solutions to the Helmholtz equation are used here. This is achieved at the expense of a restriction imposed on the size of admissible domains—a feature absent in the inverse mean value properties known previously.