Can anyone give me a hint to show the following?
Let $m$ be a positive integer and $u : \mathbb{R}^{n} \rightarrow \mathbb{R}$ be a harmonic function. If $u(x) = O(\left|x \right|)^m$ when $\left|x \right| \to \infty$, show that $u$ is polynomial of degree at most $m$.
Any clue will be great.
Thanks