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In this paper we shed new light on the AdS/CFT duality by interpreting theCFT as the Fourier space of AdS. We make use of well known integral geometrytechniques to derive the Fourier transformation of a function defined on theAdS hyperboloid. We show that the Fourier Transformation of a function on thehyperboloid is a function defined on the boundary. We find that the Green'sfunctions from the literature are actually the Fourier weights (i.e. plane wavesolutions) of the transformation and that the boundary values of fieldsappearing in the correspondence are the Fourier components of thetransformation. One is thus left to interpret the CFT as the quantized versionof a classical theory in AdS and the dual operator as the Fourier coefficients.Group theoretic considerations are discussed in relation to the transformationand its potential use in constructing QCD like theories. In addition, weconsider possible implications involving understanding the dual of AdS blackholes.

An Alternative Path to the Boundary - the CFT as the Fourier Space of AdS