  Let $\ds dA=\frac{dxdy}\pi$ denote the normalized Lebesgue area measure on
the unit disk $\disk$ and $u$, a summable function on $\disk$.
$$B(u)(z)=\int_\disk u(\zeta)\frac{(1-|z|^2)^2}{|1-\zeta\oln z|^4}dA(\zeta)$$
is called the Berezin transform of $u$. Ahern \cite{a} described all the
possible triples $\{u,f,g\}$ for which $$B(u)(z)=f(z)\oln g(z)$$ where both
$f,g$ are holomorphic in $\disk$. This result was crucial in solving a version
of the zero product problem for Toeplitz operators on the Bergman space. The
natural next question was to describe all functions in the range of Berezin
Transform which are of the form $$\sum_{i=1}^Nf_i\oln g_i$$ where $f_i,g_i$ are
all holomorphic in $\disk$. We shall give a complete description of all such
$u$ and the corresponding $f_i,g_i,1\leq i\leq N$. Further we give very simple
proof of the result of Ahern \cite{a} and the recent results of
\v{C}u\v{c}kovi\'c and Li \cite{bz} where they tackle the special case when N=2
and $g_2=z^n$.
