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

This article is cited in 2 scientific papers (total in 2 papers)

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 НШ-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. НШ-6222.2018.1).

Author to whom correspondence should be addressed

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

Full text: PDF file (578 kB)
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English version:
Sbornik: Mathematics, 2018, 209:5, 660–671

Bibliographic databases:

UDC: 517.987
MSC: 37A25, 37A30
Received: 28.02.2017 and 06.09.2017

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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    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  mathnet  crossref  crossref  isi  elib
    2. I. V. Klimov, “Simple Spectrum of Tensor Products and Typical Properties of Measure-Preserving Flows”, Math. Notes, 104:6 (2018), 927–929  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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