If for an harmonic function $u$ in $\mathbb R^n \times \mathbb R_+$, $u(\mathbf{0},y) = 0$ then $u \equiv 0$?

Question

If $u$ is a harmonic function on $\mathbb R^n \times \mathbb R_+$ and $$u(\mathbf{0},y) = 0$$ (here $\mathbf{0} \in \mathbb R^n$ and $y \in \mathbb R_+$) and $u$ depends radially on the first variable, then is it true that $u \equiv 0$?