Product ℤd-actions on a Lebesgue space and their applications
Filipowicz, I.
Studia Mathematica, Tome 122 (1997), p. 289-298 / Harvested from The Polish Digital Mathematics Library
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We define a class of ℤd-actions, d ≥ 2, called product ℤd-actions. For every such action we find a connection between its spectrum and the spectra of automorphisms generating this action. We prove that for any subset A of the positive integers such that 1 ∈ A there exists a weakly mixing ℤd-action, d≥2, having A as the set of essential values of its multiplicity function. We also apply this class to construct an ergodic ℤd-action with Lebesgue component of multiplicity 2dk, where k is an arbitrary positive integer.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216376 
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     title = {Product $$\mathbb{Z}$^d$-actions on a Lebesgue space and their applications},
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     year = {1997},
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Filipowicz, I. Product $ℤ^d$-actions on a Lebesgue space and their applications. Studia Mathematica, Tome 122 (1997) pp. 289-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i3p289bwm/

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