On the power rate of convergence in Wiener's ergodic theorem Full article
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St. Petersburg Mathematical Journal
ISSN: 1061-0022 , E-ISSN: 1547-7371 |
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| Output data | Year: 2024, Volume: 35, Number: 6, Article number : 1841, Pages count : 7 DOI: 10.1090/spmj/1841 | ||
| Tags | Bessel functions, Rates of convergence in ergodic theorems, Wiener’s ergodic theorem | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
For ergodic averages over d -dimensional balls, an integral representation is obtained for L_2 -norms with a kernel containing the Bessel functions of the first kind. Based on this formula, a spectral criterion for the power rate of convergence in Wiener’s ergodic theorem is proved for all possible exponents. The resulting criterion completely covers the known 1-dimensional result.
Cite:
Podvigin I.V.
On the power rate of convergence in Wiener's ergodic theorem
St. Petersburg Mathematical Journal. 2024. V.35. N6. 1841 :1-7. DOI: 10.1090/spmj/1841 WOS Scopus OpenAlex
On the power rate of convergence in Wiener's ergodic theorem
St. Petersburg Mathematical Journal. 2024. V.35. N6. 1841 :1-7. DOI: 10.1090/spmj/1841 WOS Scopus OpenAlex
Original:
Подвигин И.В.
О степенной скорости сходимости в эргодической теореме Винера
Алгебра и анализ. 2023. Т.35. №6. С.159–168. РИНЦ
О степенной скорости сходимости в эргодической теореме Винера
Алгебра и анализ. 2023. Т.35. №6. С.159–168. РИНЦ
Dates:
| Submitted: | Jun 28, 2023 |
| Published online: | Jan 9, 2025 |
| Published print: | Jan 10, 2025 |
Identifiers:
| Web of science: | WOS:001401294300001 |
| Scopus: | 2-s2.0-85217139508 |
| OpenAlex: | W4406270601 |
Citing:
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