  We define the holomorphic Fourier transform of holomorphic functions on
complex reductive groups, prove some properties like the Fourier inversion
formula, and give some applications. The definition of the holomorphic Fourier
transform makes use of the notion of $K$-admissible measures. We prove that
$K$-admissible measures are abundant, and the definition of holomorphic Fourier
transform is independent of the choice of $K$-admissible measures.
