Geodesic
Product $ℤ^d$-actions on a Lebesgue space and their applications
Studia Mathematica, Tome 122 (1997) no. 3, pp. 289-298

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We define a class of $ℤ^d$-actions, d ≥ 2, called product $ℤ^d$-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 $ℤ^d$-action, d≥2, having A as the set of essential values of its multiplicity function. We also apply this class to construct an ergodic $ℤ^d$-action with Lebesgue component of multiplicity $2^d k$, where k is an arbitrary positive integer.
DOI : 10.4064/sm-122-3-289-298
Mots-clés : $ℤ^d$-action, spectral theorem, spectrum, spectral multiplicity function

I. Filipowicz 1

1 
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I. Filipowicz. Product $ℤ^d$-actions on a Lebesgue space and their applications. Studia Mathematica, Tome 122 (1997) no. 3, pp. 289-298. doi: 10.4064/sm-122-3-289-298

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