Bianalytic functions with exceptional values

Abstract:

Let $f(z,\bar z)$ be a bianalytic function which omits the value zero in some deleted neighborhood $A$ of an isolated singularity ${z_0}$. It is shown that there is a function $g(z)$ analytic on $A$ and a function $h(z,\bar z)$ bianalytic on $A$ with a nonessential singularity at ${z_0}$ such that $f(z,\bar z) = g(z)h(z,\bar z)$ on $A$.