  We present a theoretical investigation of the dynamic density structure
factor of a strongly interacting Fermi gas near a Feshbach resonance at finite
temperature. The study is based on a gauge invariant linear response theory.
The theory is consistent with a diagrammatic approach for the equilibrium state
taking into account the pair fluctuation effects and respects some important
restrictions like the $f$-sum rule. Our numerical results show that the dynamic
density structure factor at large incoming momentum and at half recoil
frequency has a qualitatively similar behavior as the order parameter, which
can signify the appearance of the condensate. This qualitatively agrees with
the recent Bragg spectroscopy experiment results. We also present the results
at small incoming momentum.
