  A general framework in the setting of $C^*$-algebras for the tomographical
description of states, that includes, among other tomographical schemes, the
classical Radon transform, quantum state tomography and group quantum
tomography, is presented.
  Given a $C^*$-algebra, the main ingredients for a tomographical description
of its states are identified: A generalized sampling theory and a positive
transform. A generalization of the notion of dual tomographic pair provides the
background for a sampling theory on $C^*$-algebras and, an extension of
Bochner's theorem for functions of positive type, the positive transform.
  The abstract theory is realized by using dynamical systems, that is, groups
represented on $C^*$-algebra. Using a fiducial state and the corresponding GNS
construction, explicit expressions for tomograms associated with states defined
by density operators on the corresponding Hilbert spade are obtained. In
particular a general quantum version of the classical definition of the Radon
transform is presented. The theory is completed by proving that if the
representation of the group is square integrable, the representation itself
defines a dual tomographic map and explicit reconstruction formulas are
obtained by making a judiciously use of the theory of frames. A few significant
examples are discussed that illustrates the use and scope of the theory.
