I know that every holomporphic funcion on a Torus can be written in term of $\wp(z)$ and $\wp'(z)$. I'm however looking for a set ortogonal holomporphic function on $T^2$. That is, given an holomporphic function $f(z)$ on the torus, I would like to write it as
$$ f(z) = \sum_{m, n} a_{m, n} g_{n, m}(z) $$
And to determine the $g$'s. I know that using a Fourier basis this can be done, however that basis is not holomporphic.