  We discuss about the conjectural cohomological theory of dynamical zeta
functions in the case of general Anosov flows. Our aim is to provide a
functional-analytic framework that enables us to justify the basic part of the
theory rigorously. We show that the zeros and poles of a class of dynamical
zeta functions, including the semi-classical (or Gutzwiller-Voros) zeta
functions, are interpreted as eigenvalues of the generators of some transfer
operators acting on the leaf-wise de Rham cohomology spaces of the unstable
foliation.
