New spectral multiplicities for ergodic actions

Details New spectral multiplicities for ergodic actions New spectral multiplicities for ergodic actions

2011-09-20

arxiv.org/abs/1109.4367v1

Mathematics

Dynamical Systems

17 pages

Scientific paper

Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space, let M(T) denote the set of essential values of the spectral multiplicity function of the Koopman unitary representation of G associated with T. In the case when G is either a discrete countable Abelian group or R^n, n>0, 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) for a weakly mixing G-action T.

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