Decay of correlations in suspension semi-flows of angle-multiplying maps

We consider suspension semi-flows of angle-multiplying maps on the circle for C^r ceiling functions with r3. Under a C^rgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L² space such that the PerronFrobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the PerronFrobenius operator for the time-t-map is quasi-compact for a C^r open and dense set of ceiling functions.