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Absolute continuity and singularity of spectra for flows T_t⊗T_{at}статья
- Автор: Ryzhikov V.V.
- Журнал: ArXiv e-prints
- Номер: arXiv:2202.09336
- Год издания: 2022
- Аннотация: Answering the question of V.I. Oseledets, we present a random variable ξ such that the sum ξ(x)+aξ(y) has a singular distribution for a set of parameters a dense in (1,+∞), but for another dense set of parameters, this sum has an absolutely continuous distribution. We prove the following assertion: given C,D, countable non-intersecting dense subsets of the ray (1,+∞), there is a measure-preserving flow T_t (acting on the infinite Lebesgue space) such that automorphisms T_1⊗T_c have simple singular spectra for every c∈C, and T_1⊗T_d have Lebesgue spectra for all d∈D. The spectral measure of this flow plays the role of the distribution of our random variable ξ
- Добавил в систему: Рыжиков Валерий Валентинович