Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map (Q1871897)

One considers operators of the form \(Uf(x)=\int a(x,y) f(b(x,y)) \mu(dy)\) on functions \(f:(u,v)\to C\) (an example is the evolution operator of one-dimensional dynamical systems or Markov processes). Results for analyticity of the smooth eigenfunctions of such operators are applied for studying spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. The domain of validity of the Mayer and Röpstorff asymptotic formula for the decay of correlations of the Gauss map is extended.