Abstract
In this chapter we will discuss the spectral theory of rank one automorphisms. This is intimately related to the notion of Riesz product. We will define a class of measures on S1 called Riesz product and show that such measures appear as maximal spectral types of certain towers over adding machine. We will also define generalised Riesz products and show that such measures are related to the spectrum of general rank one automorphisms.
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