Product $ℤ^d$-actions on a Lebesgue space and their applications
Studia Mathematica, Tome 122 (1997) no. 3, pp. 289-298
Cet article a éte moissonné depuis 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.
Mots-clés :
$ℤ^d$-action, spectral theorem, spectrum, spectral multiplicity function
@article{10_4064_sm_122_3_289_298,
author = {I. Filipowicz},
title = {Product $\ensuremath{\mathbb{Z}}^d$-actions on a {Lebesgue} space and their applications},
journal = {Studia Mathematica},
pages = {289--298},
year = {1997},
volume = {122},
number = {3},
doi = {10.4064/sm-122-3-289-298},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-122-3-289-298/}
}
TY - JOUR AU - I. Filipowicz TI - Product $ℤ^d$-actions on a Lebesgue space and their applications JO - Studia Mathematica PY - 1997 SP - 289 EP - 298 VL - 122 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-122-3-289-298/ DO - 10.4064/sm-122-3-289-298 LA - fr ID - 10_4064_sm_122_3_289_298 ER -
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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