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 Mat. Sb., 2018, Volume 209, Number 5, Pages 62–73 (Mi msb8932)

Special weak limits and simple spectrum of the tensor products of flows

M. S. Lobanov, V. V. Ryzhikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: An example of a measure-preserving flow $T_t$ for which the tensor product $T_t\otimes T_{\alpha t}$ has simple spectrum for all $\alpha > 1$ is constructed. The construction of the flow uses asymptotically infinitesimal spacers and spacers obtained using results in finite field theory. For the spectral measure $\sigma$ of a flow of this type, any nonorthogonal projection of the measure $\sigma\times\sigma$ onto the diagonal in $\mathbb R\times \mathbb R$ is a 1-1 mapping $(\operatorname{mod} 0)$ with respect to the measure $\sigma\times\sigma$.
Bibliography: 12 titles.

Keywords: ergodic flow, lacunar rigidity, Galois fields, special weak limits, simple spectrum, tensor product.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÍØ-6222.2018.1 This work was supported by the Programme for State Support of Leading Scientific Schools of the President of the Russian Federation (project no. ÍØ-6222.2018.1).

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DOI: https://doi.org/10.4213/sm8932

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English version:
Sbornik: Mathematics, 2018, 209:5, 660–671

Bibliographic databases:

UDC: 517.987
MSC: 37A25, 37A30

Citation: M. S. Lobanov, V. V. Ryzhikov, “Special weak limits and simple spectrum of the tensor products of flows”, Mat. Sb., 209:5 (2018), 62–73; Sb. Math., 209:5 (2018), 660–671

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8932
• https://doi.org/10.4213/sm8932
• http://mi.mathnet.ru/eng/msb/v209/i5/p62

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904
2. I. V. Klimov, “Simple Spectrum of Tensor Products and Typical Properties of Measure-Preserving Flows”, Math. Notes, 104:6 (2018), 927–929
3. V. V. Ryzhikov, “Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum”, Math. Notes, 106:6 (2019), 957–965
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