  We extend the formalism introduced in the paper hep-th/0209050 to compute
correlation functions in the AdS/CFT correspondence. We show how the on-shell
action of a scalar field in a compactification of AdS space can be obtained by
flowing in the space of (non-local) theories with different sizes of the
extra-dimension. Our method is relevant in particular for holographic
computations in the Randall-Sundrum scenario with one or two branes and it
allows the inclusion of brane-localized actions in a systematic way. The method
can also be generalized to other backgrounds and does not rely on explicit
knowledge of the solutions of the wave-equations.
