  Adapting tools that we introduced in [19] to study Anosov flows, we prove
that the trace formula conjectured by Dyatlov and Zworski in [12] holds for
Anosov flows in a certain class of regularity (smaller than
$\mathcal{C}^\infty$ but larger than the class of Gevrey functions). The main
ingredient of the proof is the construction of a family of anisotropic Hilbert
spaces of generalized distributions on which the generator of the flow has
discrete spectrum.
