Wiener-Hopf filtering in Hilbert resolution space

The theory of causal operators defined on a Hilbert resolution space is employed to derive an abstract Wiener-Hopf filter. The resultant derivation is formally identical to the classical frequency-domain derivation of the Wiener-Hopf filter for linear time-invariant lumped systems though, by virtue of the abstract setting, the resultant filter is applicable to distributed, time-variable, and finite-time problems.