Berenstein, Carlos A.Tarabusi, E. CasadioWe study the relation between convolution operators and the totally geodesic Radon transform on hyperbolic spaces. as an application we show that the linearized inverse conductivity problem in the disk can be interpreted exactly in terms of the X- ray transform with respect to the Poincare metric and of a simple convolution operator.en-USalgorithmsIntelligent Control SystemsTechnical Report