|
ИСТИНА |
Войти в систему Регистрация |
Интеллектуальная Система Тематического Исследования НАукометрических данных |
||
Spectra of Self-Similar Ergodic Actionsстатья
- Автор: Рыжиков В.В.
- Журнал: Mathematical Notes
- Том: 113
- Номер: 2
- Год издания: 2023
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 113
- Последняя страница: 120
- DOI: 10.1134/S0001434623010303
- Аннотация: —Self-similar constructions of transformations preserving a sigma-finite measure areconsidered and their properties and the spectra of the induced Gaussian and Poisson dynamicalsystems are studied. The orthogonal operator corresponding to such a transformation has theproperty that some power of this operator is a nontrivial direct sum of operators isomorphic to the original one. The following results are obtained. For any subset M of the set of positive integers, inthe class of Poisson suspensions, sets of spectral multiplicities of the form M ∪ {∞} are realized. AGaussian flow S_t is presented such that the set of spectral multiplicities of the automorphisms S^p^nis {1, ∞} if n ≤ 0 and {p^n, ∞} if n > 0. A Gaussian flow T_t such that the automorphisms T^p^nhave distinct spectral types for n ≤ 0 but all automorphisms T_p_n , n > 0, are pairwise isomorphic is constructed.
- Добавил в систему: Рыжиков Валерий Валентинович