RELATIVISTIC ELECTRON-ENERGY SPECTRA OF ACTIVE GALACTIC NUCLEI IN THETHIN SYNCHROTRON LIMIT .1. THE METHOD

Here we present a new method called ''inverse synchrotron transform'' (IST) to study the spectral energy distributions of active galactic nu clei. We demonstrate that it is possible to make use of Bayes Theorem for conditional probablility in order to derive a unique, self-consist ent solution for the electron energy spectra (EES), departing from the observed spectral energy distributions (SED) and the assumption that the main physical process involved is the emission of thin synchrotron radiation. We show the close relationship between the EES so derived, and the electron energy distribution (EED), which in turn, does not h ave a unique solution, but depends on assumptions that fix the magneti c field strength. We test the IST method and find that it is capable o f distinguishing between rather different EEDs that produce SEDs that are apparently very similar.