Titlebook: Spectral Theory of Dynamical Systems; M. G. Nadkarni Book 1998 Hindustan Book Agency 1998

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Baire Category Theorems of Ergodic Theory,In this chapter we will describe a topology on the class of non-singular automorphisms on a measure space and discuss the Baire category of some naturally occurring subclasses of it. We shall make a similar study of the class of measure preserving automorphisms.

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Additional Topics,In this chapter we treat some additional interesting topics. We first prove a theorem due to V. M. Alexeyev showing the existence of a bounded function with maximal spectral type.

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,B. Host’s Theorem,ng of . and . if . is invariant under . × .: (., .) → (., .), and the projection of . on . is . and on . is .. The product measure . × . is a joining of . and . but the systems may admit other joinings. The measure . × . is called the independent joining of . and ..

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Generalities on Systems of Imprimitivity,th . (defined by ... = .(.. .), satisfies with . the relation.In this chapter we consider such a relation in a general setting. We will discuss spectral measures on a Borel space (., .) and groups of unitary operators which together satisfy a relation similar to above. Such systems are called systems of imprimitivity, (see V. S. Varadarajan [5]).

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A Theorem of Helson and Parry,nd consider the unitary operator .. defined on ..(., ., .) by.In a paper entitled “Cocycles and Spectra” [3], Helson and Parry prove that for every aperiodic . there exists a function . such that the maximal spectral type of .. is Lebesgue; moreover . can be chosen to be real, i.e., taking values −1