Abstract

In this chapter we prove some new results about generalized Riesz products bringing into consideration the Hardy class theory, the notion of Mahler measure, and the zeros of polynomials appearing in the generalized Riesz product. A natural formula for the Radon Nykodym derivative between two generalized Riesz products is established under suitable conditions. This is then used to formulate a dichotomy theorem and prove a conditional version of it. A discussion involving spectrum of non-singular automorphisms, flat polynomials and Banach's problem about the existence of an automorphism with simple Lebesgue spectrum is given.

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