  A theorem for the invertibility of arbitrary response functions is presented
under the following conditions: the time-dependence of the potentials should be
Laplace transformable and the initial state should be a ground state, though it
might be degenerate. This theorem provides a rigorous foundation for all
density-functional-like theories in the time-dependent linear response regime.
Especially for time-dependent one-body reduced density matrix (1RDM) functional
theory this is an important step forward, since a solid foundation has
currently been lacking. The theorem is equally valid for static response
functions in the non-degenerate case, so can be used to characterize the
uniqueness of the potential in the ground state version of the corresponding
density-functional-like theory. Such a classification of the uniqueness of the
non-local potential in ground state 1RDM functional theory has been lacking for
decades. With the aid of presented invertibility theorem presented here, a
complete classification of the non-uniqueness of the non-local potential in
1RDM functional theory can be given for the first time.
