  In this paper we shed new light on the AdS/CFT duality by interpreting the
CFT as the Fourier space of AdS. We make use of well known integral geometry
techniques to derive the Fourier transformation of a function defined on the
AdS hyperboloid. We show that the Fourier Transformation of a function on the
hyperboloid is a function defined on the boundary. We find that the Green's
functions from the literature are actually the Fourier weights (i.e. plane wave
solutions) of the transformation and that the boundary values of fields
appearing in the correspondence are the Fourier components of the
transformation. One is thus left to interpret the CFT as the quantized version
of a classical theory in AdS and the dual operator as the Fourier coefficients.
Group theoretic considerations are discussed in relation to the transformation
and its potential use in constructing QCD like theories. In addition, we
consider possible implications involving understanding the dual of AdS black
holes.
