Let $U\subset \mathbb{C}^n$ be a domain. Consider $A^2(U)=L^2(U)\cap \mathcal{O}(U)$.
Fix $z_0\in U$. For $\alpha \in (\mathbb{Z}\cup{0})^n$ define $$m_{\alpha,z_0}=inf\{||f||: f\in A^2(U), f^\alpha(z_0)=1, f^\beta(z_0)=0, \forall \beta <\alpha\}$$
[ Here we say $\beta < \alpha$ when either $|\beta|<|\alpha|$, or $|\beta|=|\alpha|$ and $\beta_j<\alpha_j$, $\beta_i=\alpha_i$, $\forall$ $i<j$. ]
We can show that there $\textbf{exists a unique}$ function in $A^2(U)$, which minimizes the above norm. Call that minimal function as $K_{\alpha,z_0}(z)$.
$$\textbf{Show that } \{K_{\alpha,z_0}(\cdot)/||K_{\alpha,z_0}||\}_{\alpha} \textbf{ forms a orthonormal basis.}$$
Clearly if $f=\sum c_{\alpha} K_{\alpha,z_0}$(as a formal sum), then it is clear that $c_\alpha$ is uniquely determined.
However, I am not able to show that the sum converges to $f$. I would be grateful if you could give me a reference for this.
Thanks in advance.