## Taiwanese Journal of Mathematics

### ON DOMINATING PHENOMENON FOR BOUNDED REAL HARMONIC FUNCTIONS IN SEVERAL VARIABLES

#### 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 $h^\infty(\Re{B_n})$, on the open unit ball $\Re{B_n}$ in $\mathbb{R}^n$, $n \geq 3$, and for bounded real $\mathcal{M}$-harmonic functions, denoted by $\mathcal{M} h^\infty(B_n)$, on the open unit ball $B_n$ in $\mathbb{C}^n$, $n \ge 2$.

#### Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 501-515.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405804

Digital Object Identifier
doi:10.11650/twjm/1500405804

Mathematical Reviews number (MathSciNet)
MR2655784

Zentralblatt MATH identifier
1202.31004

#### Citation

Chen, So-Chin; Lu, Cin-Chang. ON DOMINATING PHENOMENON FOR BOUNDED REAL HARMONIC FUNCTIONS IN SEVERAL VARIABLES. Taiwanese J. Math. 14 (2010), no. 2, 501--515. doi:10.11650/twjm/1500405804. https://projecteuclid.org/euclid.twjm/1500405804

#### References

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