Abstract
In this article, motivated by the work of Brown, Shields, and Zeller[2], we first consider the representation problem of zero by exponential sums in several complex variables. Then we give a complete characterization of dominating sets for bounded real harmonic functions, denoted by h ∞ (RB n ), on the open unit ball RB n in R n , n ≥ 3, and for bounded real M-harmonic functions, denoted by Mh ∞ (B n ), on the open unit ball B n in C n , n ≥ 2.