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arXiv · 1902.03215

Spectral properties and approximations of joinings for infinite rank-one actions

V. V. Ryzhikov
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Abstract

An ergodic self-joining of an infinite rank-one transformation is a part of the weak limit of off-diagonal measures. A class of uncountaible cardinality of nonisomorphic transformations with polynomial weak closure is presented. Such actions have minimal self-joinings and some unusual spectral properties. For any set $M$ of positive integers there exists an infinite transformation $T$ such that the products $T\otimes T^m$ have simple singular spectrum as $1<m\in M$, and Lebesgue spectrum as $1<m\notin M$. There are similar effects for the corresponding Gaussian and Poisson suspensions.

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V. V. Ryzhikov. 2019-02-08. Spectral properties and approximations of joinings for infinite rank-one actions. https://arxiv.org/abs/1902.03215

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