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Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space (X,μ), let ℳ (T) denote the set of essential values of the spectral multiplicity function of the Koopman representation of G defined in L²(X,μ) ⊖ ℂ by . If G is either a discrete countable Abelian group or ℝⁿ, n ≥ 1, it is shown that the sets of the form p,q,pq, p,q,r,pq,pr,qr,pqr etc. or any multiplicative (and additive) subsemigroup of ℕ are realizable as ℳ (T)...
We construct a rank-one infinite measure preserving flow such that for each p > 0, the “diagonal” flow on the product space is ergodic.
Via the (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.
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