  The Fock space of bosons and fermions and its underlying superalgebra are
represented by algebras of functions on a superspace. We define Gaussian
integration on infinite dimensional superspaces, and construct superanalogs of
the classical function spaces with a reproducing kernel -- including the
Bargmann-Fock representation -- and of the Wiener-Segal representation. The
latter representation requires the investigation of Wick ordering on Z2-graded
algebras. As application we derive a Mehler formula for the Ornstein-Uhlenbeck
semigroup on the Fock space.
