Abstract
Unitary flows \(T_t\) of dynamical origin such that, for any countable \(Q\subset (0,+\infty)\), the spectrum of the tensor product \(\bigotimes_{q\in Q} T_q \) is simple are constructed. All typical flows preserving a sigma-finite measure have this property.
References
O. Ageev, Invent. Math., 160:2 (2005), 417–446.
E. Glasner, J.-P. Thouvenot, and B. Weiss, Proceedings Mosk. Mat. O-va, 82:1 (2021), 19–44.
I. V. Klimov, Mat. Zametki, 104:6 (2018), 942–944; English transl.: Math. Notes, 104:6 (2018), 927–929.
I. P. Cornfeld, S. V. Fomin, and Y. G. Sinai, Ergodic Theory, Springer, New York, 1982.
M. S. Lobanov and V. V. Ryzhikov, Mat. Sb., 209:5 (2018), 62–73; Sb. Math., 209:5 (2018), 660–671.
S. V. Tikhonov, Mat. Sb., 197:1 (2006), 97–132; English transl.: Sb. Math., 197:1 (2006), 95–126.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2022, Vol. 56, pp. 113–117 https://doi.org/10.4213/faa4011.
Translated by O. V. Sipacheva
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Ryzhikov, V.V. Unitary Flows with Tensor Simple Spectrum. Funct Anal Its Appl 56, 327–330 (2022). https://doi.org/10.1134/S0016266322040116
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DOI: https://doi.org/10.1134/S0016266322040116