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This article is cited in 5 scientific papers (total in 5 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm12303https://doi.org/10.4213/mzm12303 https://www.mathnet.ru/eng/mzm/v106/i6/p894
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Abstract page: | 249 | Full-text PDF : | 22 | References: | 25 | First page: | 3 |
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