  We consider the coupled set of spectral Dyson-Schwinger equations in
Yang-Mills theory for ghost and gluon propagators, which gives us access to the
ghost and gluon spectral functions. The set-up is used for a systematic
analytic evaluation of the constraints on generalised spectral representations
in Yang-Mills theory that are most relevant for informed spectral
reconstructions. We also provide numerical results for the coupled set of
spectral functions for a large range of potential mass gaps of the gluon, and
discuss the limitations and extensions of the present work.
