Functional N-representability in density matrix and density functional theory

We discuss the problem of functional N-representability both in density-matrix theory and density functional theory. For the case of the 1-matrix, we show that functional N-representability imposes conditions on the reduced single-particle operator as well as on the 1-matrix. We illustrate this point by applying a constructive method in order to obtain a functionally pure-state N-representable single-particle operator acting on an ensemble N-representable 1-matrix. For the case of density functional theory, we deal with functional N-representability in terms of local scaling transformations. An exact functional for Hooke's atom generated using these transformations is presented.