In this paper we introduce Hilbert spaces of holomorphic functions given by
generalized Borel and Laplace transforms which are left invariant by the
transfer operators of the Farey map and its induced version, the Gauss map,
respectively. By means of a suitable operator-valued power series we are able
to study simultaneously the spectrum of both these operators along with the
analytic properties of the associated dynamical zeta functions.Comment: 23 page