Some new cases of realization of spectral multiplicity function for ergodic transformations

• Autorzy: A. Katok , M. Lemańczyk
• Języki publikacji: EN

Abstrakty

EN

Given a countable Abelian group 𝔾, its automorphism w for which $w^{M} = Id$, and a subgroup 𝔽 ⊂ 𝔾 we define
$M(𝔾,w,𝔽) = {♯({w^{i}χ: i ∈ ℤ ∩ 𝔽): χ ∈ 𝔽∖{0}}$.
We prove that each finite set of the form M(𝔾,w,𝔽) ∪ {2} is realized as the set of essential values of the multiplicity function of the Koopman operator of some weakly mixing automorphism.

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 37A05: Measure-preserving transformations
• 28D05: Measure-preserving transformations
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 206
• Numer: 1
• Strony: 185-215

Daty

wydano

2009

Twórcy

autor

A. Katok

• Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.

autor

M. Lemańczyk

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/fm206-0-11