- Tytuł:
- Product $ℤ^d$-actions on a Lebesgue space and their applications
- Autorzy:
- Filipowicz, I.
- Powiązania:
- https://bibliotekanauki.pl/articles/1220208.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
$ℤ^d$-action
spectral theorem
spectrum
spectral multiplicity function - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1997, 122, 3; 289-298
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł