Complete spectral data for analytic Anosov maps of the torus

Using analytic properties of Blaschke factors we construct a family of analytic hyperbolic diffeomorphisms of the torus for which the spectra of the associated transfer operator acting on a suitable Hilbert space can be computed explicitly. As a result, we obtain expressions for the decay of correlations of analytic observables without resorting to any kind of perturbation argument.