  In this paper we display a family of Gaussian processes, with explicit
formulas and transforms. This is presented with the use of duality tools in
such a way that the corresponding path-space measures are mutually singular. We
make use of a corresponding family of representations of the canonical
commutation relations (CCR) in an infinite number of degrees of freedom.
  A key feature of our construction is explicit formulas for associated
transforms; these are infinite-dimensional analogues of Fourier transforms. Our
framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert
spaces, and Fock spaces. The latter forms the setting for our CCR
representations. We further show, with the use of representation theory, and
infinite-dimensional analysis, that our pairwise inequivalent probability
spaces (for the Gaussian processes) correspond in an explicit manner to
pairwise disjoint CCR representations.
