The spectral representation of stable processes: Harmonizability and regularity

Summary We show that symmetric -stable moving average processes are not harmonizable. However, we show that a concept of generalized spectrum holds for allL _p -bounded processes O<p<-2. In capep=2, generalized spectrum is a measure and the classical representation follows. For strongly harmonizable symmetric -stable processes we derive necessary and sufficient conditions for the regularity and the singularity for 0<2, using known results on the invariant subspaces. We also get Cramér-Wold decomposition for the case 0<2.Supported by CPBP01. 02.Supported by ONR N00014-85-K-0150