Let $P \in \mathcal{P}$. Show that $P$ decomposes uniquely in the form: $$P(x,y) = H(x,y) + (1 - x^2 - y^2) Q(x,y)$$ where $H$ is a harmonic polynomial and $Q \in \mathcal{P}$.
Let $P \in \mathcal{P}$. Show that $P$ decomposes uniquely in the form:
$$P(x,y) = H(x,y) + (1 - x^2 - y^2) Q(x,y)$$
where $H$ is a harmonic polynomial and $Q \in \mathcal{P}$.