  Suppose $A$ is a positive real linear transformation on a finite dimensional
complex inner product space $V$. The reproducing kernel for the Fock space of
square integrable holomorphic functions on $V$ relative to the Gaussian measure
$d\mu_A(z)=\frac {\sqrt {\det A}} {\pi^n}e^{-{\rm Re}< Az,z>} dz$ is described
in terms of the holomorphic--antiholomorphic decomposition of the linear
operator $A$. Moreover, if $A$ commutes with a conjugation on $V$, then a
restriction mapping to the real vectors in $V$ is polarized to obtain a
Segal--Bargmann transform, which we also study in the Gaussian-measure setting.
