  We show that every multiparameter Gaussian process with integrable variance
function admits a Wiener integral representation of Fredholm type with respect
to the Brownian sheet. The Fredholm kernel in the representation can be
constructed as the unique symmetric square root of the covariance. We analyze
the equivalence of multiparameter Gaussian processes by using the Fredholm
representation and show how to construct series expansions for multiparameter
Gaussian processes by using the Fredholm kernel.
