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

A. Katok; M. Lemańczyk

doi:10.4064/fm206-0-11

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

A. Katok, M. Lemańczyk

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Given a countable Abelian group G, its automorphism ω for which ω = Id, and a subgroup F ⊂ G we define (equation presented). We prove that each finite set of the form M (G, ω, F) ∪ {2} is realized as the set of essential values of the multiplicity function of the Koopman operator of some weakly mixing automorphism.

Original language	English (US)
Pages (from-to)	185-215
Number of pages	31
Journal	Fundamenta Mathematicae
Volume	206
Issue number	1
DOIs	https://doi.org/10.4064/fm206-0-11
State	Published - 2009

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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AB - Given a countable Abelian group G, its automorphism ω for which ω = Id, and a subgroup F ⊂ G we define (equation presented). We prove that each finite set of the form M (G, ω, F) ∪ {2} is realized as the set of essential values of the multiplicity function of the Koopman operator of some weakly mixing automorphism.

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

Abstract

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