The Identification Problem for complex-valued Ornstein-Uhlenbeck operators in Lp(Rd,CN)

for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. We prove under certain conditions that the maximal domain D(Ap) of the generator Ap belonging to the OrnsteinUhlenbeck semigroup coincides with the domain of L∞ in L (R,C) given by D loc (L0) = {