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. 
@article{MZM_2019_106_6_a9,
     author = {V. V. Ryzhikov},
     title = {Weak {Closure} of {Infinite} {Actions} of {Rank~1,} {Joinings,} and {Spectrum}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {894--903},
     publisher = {mathdoc},
     volume = {106},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a9/}
}
TY  - JOUR
AU  - V. V. Ryzhikov
TI  - Weak Closure of Infinite Actions of Rank~1, Joinings, and Spectrum
JO  - Matematičeskie zametki
PY  - 2019
SP  - 894
EP  - 903
VL  - 106
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a9/
LA  - ru
ID  - MZM_2019_106_6_a9
ER  - 
%0 Journal Article
%A V. V. Ryzhikov
%T Weak Closure of Infinite Actions of Rank~1, Joinings, and Spectrum
%J Matematičeskie zametki
%D 2019
%P 894-903
%V 106
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a9/
%G ru
%F MZM_2019_106_6_a9
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/