Spectral decomposition of piecewise linear monotonic maps

We construct a generalized spectral decomposition of the Frobenius-Perron operator for one class of piecewise linear monotonic maps by using a general, iterative, operator method which is applicable in principle for any mixing dynamical system. The Jordan block structure is specified and analyzed. The eigenvalues in the decomposition are related to the decay rates of the correlation functions. We explicitly define appropriate generalized function spaces, which provide mathematical meaning to the spectral decomposition.