Weak closure of infinite actions of rank 1, joinings, and spectrum

DOI10.1134/S0001434619110312zbMath1439.37005OpenAlexW2997987780WikidataQ126472150 ScholiaQ126472150MaRDI QIDQ2304511

V. V. Ryzhikov

Publication date: 12 March 2020

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434619110312

zbMATH Keywords

spectrumweak closuremeasure-preserving transformationsminimal self-joiningactions of rank 1

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodicity, mixing, rates of mixing (37A25) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (4)

Mixing sets for rigid transformations ⋮ Absolute continuity and singularity of spectra for the flows \(T_t\otimes T_{at}\) ⋮ Measure-preserving rank one transformations ⋮ Polyhomomorphisms of locally compact groups

Cites Work

• Simple spectrum of tensor products and typical properties of measure-preserving flows
• On the centralizer of an infinite mixing rank-one transformation
• An example of a measure preserving map with minimal self-joinings, and applications
• Theory of dynamical systems and general transformation groups with invariant measure
• Minimal self-joinings of infinite mixing actions of rank 1
• On ergodic transformations with homogeneous spectrum
• An automorphism with simple, continuous spectrum not having the group property
• Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions
• The commutant is the weak closure of the powers, for rank-1 transformations
• On the correspondence between boson Fock space and theL²space with respect to Poisson measure
• Special weak limits and simple spectrum of the tensor products of flows

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