  Aulbach et al. (2012) introduced the concept of D-norms in the framework of
functional extreme value theory (EVT) extending the multivariate case in a
natural manner. In particular, the distribution of a standard max-stable
process (MSP) {\eta} \in C[0,1] is completely determined by its functional
distribution function, which itself is given by some D-norm.
  In order to generate a generalized Pareto process (GPP) that is in the
functional domain of attraction of {\eta}, one may use the fact that every
D-norm is defined by some generator process with continuous sample paths. It
is, however, still unknown which generator must be chosen such that a given
D-norm arises. This is the content of the present paper. We will, moreover,
show that a generator process may be decomposed into a functional deterministic
part and a univariate random one.
