  In this work, we strive to gain insight into thermal modifications of
charmonium and bottomonium bound states as well as the heavy quark diffusion
coefficient. The desired information is contained in the spectral function
which can not be calculated on the lattice directly. Instead, the correlator
given by an integration over the spectral function times an integration kernel
is obtained. Extracting the spectral function is an ill-posed inversion problem
and various different solutions have been proposed. We focus on a comparison to
a spectral function obtained from combining perturbative and pNRQCD
calculations. In order to get precise results, continuum extrapolated
correlators originating from large and fine lattices are used. We first analyze
the pseudoscalar channel since the absence of a transport peak simplifies the
analysis. The knowledge gained from this is then used to extend the analysis to
the vector channel, where information on heavy quark transport is encoded in
the low frequency regime of the spectral function. The comparison shows a
qualitatively good agreement between perturbative and lattice correlators.
Quantitative differences can be explained by systematic uncertainties.
