Geodesic
Weak Closure of Infinite Actions of Rank~1, Joinings, and Spectrum
Matematičeskie zametki, Tome 106 (2019) no. 6, pp. 894-903.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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V. V. Ryzhikov. Weak Closure of Infinite Actions of Rank~1, Joinings, and Spectrum. Matematičeskie zametki, Tome 106 (2019) no. 6, pp. 894-903. http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a9/

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