Spectral and mixing properties of actions of amenable groups

Nir Avni

doi:10.1090/S1079-6762-05-00147-2

Spectral and mixing properties of actions of amenable groups

Nir Avni^*

^*Corresponding author for this work

Mathematics

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

5 Scopus citations

Abstract

We generalize two theorems about K-automorphisms from ℤ to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union of compact subgroups). The first theorem is that such actions are uniformly mixing; the second is that their spectrum is Lebesgue with countable multiplicity. For the proof we will develop an entropy theory for discrete amenable equivalence relations.

Original language	English (US)
Pages (from-to)	57-63
Number of pages	7
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	11
Issue number	7
DOIs	https://doi.org/10.1090/S1079-6762-05-00147-2
State	Published - Jun 10 2005

ASJC Scopus subject areas

General Mathematics

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abstract = "We generalize two theorems about K-automorphisms from ℤ to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union of compact subgroups). The first theorem is that such actions are uniformly mixing; the second is that their spectrum is Lebesgue with countable multiplicity. For the proof we will develop an entropy theory for discrete amenable equivalence relations.",

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AB - We generalize two theorems about K-automorphisms from ℤ to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union of compact subgroups). The first theorem is that such actions are uniformly mixing; the second is that their spectrum is Lebesgue with countable multiplicity. For the proof we will develop an entropy theory for discrete amenable equivalence relations.

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Spectral and mixing properties of actions of amenable groups

Abstract

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