The homogeneous spectrum problem in ergodic theory

DOI10.1007/s00222-004-0422-zzbMath1064.37003OpenAlexW1991312187MaRDI QIDQ1775151

O. N. Ageev

Publication date: 4 May 2005

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-004-0422-z

zbMATH Keywords

measure-preserving transformationRokhlin's problem

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical aspects of measure-preserving transformations (37A05) Ergodic theorems, spectral theory, Markov operators (37A30)

Related Items (15)

Smooth diffeomorphisms with homogeneous spectrum and disjointness of convolutions ⋮ New spectral multiplicities for mixing transformations ⋮ Spectral multiplicities of infinite measure preserving transformations ⋮ Special weak limits and simple spectrum of the tensor products of flows ⋮ Spectral doubling of normal operators and connections with antiunitary operators ⋮ Unitary flows with tensor simple spectrum ⋮ Homogeneous spectrum and mixing transformations ⋮ Asymptotic Abelianness, weak mixing, and property T ⋮ Mixing with staircase multiplicity functions ⋮ A survey on spectral multiplicities of ergodic actions ⋮ Spectral rigidity of group actions: Applications to the case gr⟨𝑡,𝑠;𝑡𝑠=𝑠𝑡²⟩ ⋮ Measure-preserving rank one transformations ⋮ Generic properties of extensions ⋮ Simple spectrum of the tensor product of powers of a mixing automorphism ⋮ Approximation of mixing transformations

Cites Work

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• DYNAMICAL SYSTEMS WITH AN EVEN-MULTIPLICITY LEBESGUE COMPONENT IN THE SPECTRUM
• Generic Spectral Properties of Measure-Preserving Maps and Applications
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• On the multiplicity function of ergodic group extensions, II
• Commuting point transformations
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