Abstract
We will complete the calculation of Ruelle resonances of a compact hyperbolic surface, started in the last lecture, using the representation theory of PSL(2, R). The case of principal series will be treated in detail. We'll calculate the Fourier coefficients of resonant states and deduce that they belong to negative Sobolev spaces. This will be followed by a brief presentation of the theory of anisotropic Sobolev spaces, in order to compare the results obtained by the two methods (representation theory / anisotropic spaces).
