  We provide a framework for calculating holographic Green's functions from
general bilinear actions and fields obeying coupled differential equations in
the bulk. The matrix-valued spectral function is shown to be independent of the
radial bulk coordinate. Applying this framework we improve the analysis of
fluctuations in the D3/D7 system at finite baryon density, where the
longitudinal perturbations of the world-volume gauge field couple to the scalar
fluctuations of the brane embedding. We compute the spectral function and show
how its properties are related to the quasinormal mode spectrum. We study the
crossover from the hydrodynamic diffusive to the reactive regime and the
movement of quasinormal modes as functions of temperature and density. We also
compute their dispersion relations and find that they asymptote to the
lightcone for large momenta.
