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Product $ℤ^d$-actions on a Lebesgue space and their applications

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Filipowicz I.

Studia Mathematica

1997

tom 122

nr 3

289-298

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.

Ograniczanie wyników

1 Studia Mathematica

1 Filipowicz I.

1 1997

Wyniki wyszukiwania

Product $ℤ^d$-actions on a Lebesgue space and their applications