  In recent years, there has been considerable interest in theories formulated
in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally
hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS
spacetime need not have a well defined dynamics. Nevertheless, AdS spacetime is
static, so the possible rules of dynamics for a field satisfying a linear wave
equation are constrained by our previous general analysis--given in paper
II--where it was shown that the possible choices of dynamics correspond to
choices of positive, self-adjoint extensions of a certain differential
operator, $A$. In the present paper, we reduce the analysis of electromagnetic,
and gravitational perturbations in AdS spacetime to scalar wave equations. We
then apply our general results to analyse the possible dynamics of scalar,
electromagnetic, and gravitational perturbations in AdS spacetime. In AdS
spacetime, the freedom (if any) in choosing self-adjoint extensions of $A$
corresponds to the freedom (if any) in choosing suitable boundary conditions at
infinity, so our analysis determines all of the possible boundary conditions
that can be imposed at infinity. In particular, we show that other boundary
conditions besides the Dirichlet and Neumann conditions may be possible,
depending on the value of the effective mass for scalar field perturbations,
and depending on the number of spacetime dimensions and type of mode for
electromagnetic and gravitational perturbations.
