  The possible in-medium changes of the properties of an omega meson placed in
cold nuclear matter are constrained by QCD sum rules. It is shown that the sum
rules cannot fully determine the in-medium spectral shape of the omega meson.
However, for a given parameterization the sum rules can constrain or correlate
the hadronic parameters. It is shown that weighted finite energy sum rules
provide a proper framework to study directly these constraints/correlations.
Two typical parameterizations of possible in-medium omega spectra are analyzed,
namely (i) a one-peak structure with arbitrary position and width of the peak
and (ii) a structure with two (narrow) peaks, caused by the genuine omega meson
and a resonance-hole branch. The sum rules provide for case (i) a mass-width
correlation and for case (ii) a correlation between the peak heights and the
peak position of the omega branch. It is also analyzed how the obtained results
depend on the size of the relevant four-quark operator evaluated with respect
to a nucleon. Finally it is argued that a strict vector meson dominance
scenario is not compatible with the sum rules.
