Functional representations for Fock superalgebras

The Fock space of bosons and fermions and its underlying superalgebra are r epresented by algebras of functions on a superspace. We define Gaussian int egration on infinite-dimensional superspaces, and construct super-analogs o f the classical function spaces with a reproducing kernel - including the B argmann-Fock representation - and of the Wiener-Segal representation. The l atter representation requires the investigation of Wick ordering on Z(2)-gr aded algebras. As application we derive a Mehler formula for the Ornstein-U hlenbeck semigroup on the Fock space.