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) for a weakly mixing G-action T.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-3,
author = {Anton V. Solomko},
title = {New spectral multiplicities for ergodic actions},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {229-247},
zbl = {1254.37003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-3}
}
Anton V. Solomko. New spectral multiplicities for ergodic actions. Studia Mathematica, Tome 209 (2012) pp. 229-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm208-3-3/