Riesz products and spectral decompositions for rank 1 measure preserving transformations

Abstract: We consider rank one measure preserving transformations $g$ and the corresponding unitary operators $U(g)$. It is known that a generic (in the sense of Baire category) measure preserving transformation has rank one, spectral type of $U(g)$ is purely singular and is given by a Riesz product. We write explicitly spectral decompositions of $U(g)$.