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This article is cited in 33 scientific papers (total in 33 papers)
Weak limits of powers, simple spectrum of
symmetric products, and rank-one mixing constructions
V. V. Ryzhikov M. V. Lomonosov Moscow State University
Abstract:
A class of automorphisms of the Lebesgue space such that their
symmetric powers have simple spectrum is considered. In the framework of rank-one constructions mixing automorphisms with this property are constructed. The paper also contains results on weak limits, the local rank, and the spectral multiplicity of powers of automorphisms. Spectral properties of the stochastic Chacon automorphism are discussed.
Bibliography: 23 titles.
Received: 03.10.2006 and 13.11.2006
Citation:
V. V. Ryzhikov, “Weak limits of powers, simple spectrum of
symmetric products, and rank-one mixing constructions”, Sb. Math., 198:5 (2007), 733–754
Linking options:
https://www.mathnet.ru/eng/sm3729https://doi.org/10.1070/SM2007v198n05ABEH003857 https://www.mathnet.ru/eng/sm/v198/i5/p137
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