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Mat. Zametki, 2019, Volume 106, Issue 6, Pages 894–903 (Mi mz12303)  

Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum

V. V. Ryzhikov

Lomonosov Moscow State University

Abstract: It is proved that the ergodic self-joining of an infinite transformation of rank $1$ is part of the weak limit of shifts of a diagonal measure. A continuous class of nonisomorphic transformations with polynomial closure is proposed. These transformations possess minimal self-joinings and certain unusual spectral properties. Thus, for example, the tensor products of the powers of transformations have both a singular and a Lebesgue spectrum, depending on the choice of the power.

Keywords: measure-preserving transformations, weak closure, actions of rank $1$, minimal self-joining, spectrum.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
This work was supported by the Presidential Program for the State Support of Leading Scientific Schools under grant NSh-6222.2018.1.


DOI: https://doi.org/10.4213/mzm12303

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English version:
Mathematical Notes, 2019, 106:6, 957–965

Bibliographic databases:

UDC: 517.9
Received: 31.12.2018

Citation: V. V. Ryzhikov, “Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum”, Mat. Zametki, 106:6 (2019), 894–903; Math. Notes, 106:6 (2019), 957–965

Citation in format AMSBIB
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