Эргодическая теорема фон Неймана и суммы Фейера зарядов на окружности Full article
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Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2020, Volume: 17, Pages: 1313-1321 Pages count : 9 DOI: 10.33048/semi.2020.17.097 | ||||
| Tags | deviations of Fejer sums; integral Holder condition; rates of convergence in von Neumann's ergodic theorem | ||||
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Abstract:
The Fejer sums for measures on the circle and the norms of the deviations from the limit in von Neumann’s ergodic theorem are calculated, in fact, using the same formulas (by integrating the Fejer kernels) - and so, this ergodic theorem is a statement about the asymptotics of the Fejer sums at zero for the spectral measure of the corresponding dynamical system. It made it possible, having considered the integral Holder condition for signed measures, to prove a theorem that unifies both following well-known results: classical S.N. Bernstein’s theorem on polynomial deviations of the Fejer sums for Holder functions - and theorem about polynomial rates of convergence in von Neumann’s ergodic theorem.
Cite:
Качуровский А.Г.
, Лапштаев М.Н.
, Хакимбаев А.Ж.
Эргодическая теорема фон Неймана и суммы Фейера зарядов на окружности
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2020. Т.17. С.1313-1321. DOI: 10.33048/semi.2020.17.097 WOS Scopus РИНЦ MathNet OpenAlex
Эргодическая теорема фон Неймана и суммы Фейера зарядов на окружности
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2020. Т.17. С.1313-1321. DOI: 10.33048/semi.2020.17.097 WOS Scopus РИНЦ MathNet OpenAlex
Identifiers:
| Web of science: | WOS:000571214000001 |
| Scopus: | 2-s2.0-85099343848 |
| Elibrary: | 44726608 |
| MathNet: | semr1291 |
| OpenAlex: | W3114367258 |
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