Explicit estimate of the convergence rate in the Riemann localization principle
- Authors: Popov A.Y.1,2, Semenova T.Y.1,2
-
Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 89, No 6 (2025)
- Pages: 162-182
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/358693
- DOI: https://doi.org/10.4213/im9690
- ID: 358693
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Abstract
The convergence rate in the Riemann localization principle for trigonometric series is estimated.
S. A. Telyakovskii's result for integrable functions is refined.
Functions with$\operatorname{Lip}\alpha$ integral modulus of continuity and functions of bounded variation
are considered.
S. A. Telyakovskii's result for integrable functions is refined.
Functions with
are considered.
About the authors
Anton Yur'evich Popov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Email: aypopov.msu@yandex.ru
Doctor of physico-mathematical sciences, Head Scientist Researcher
Tatyana Yurevna Semenova
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied MathematicsCandidate of physico-mathematical sciences, Associate professor
References
- E. Hille, G. Klein, “Riemann's localization theorem for Fourier series”, Duke Math. J., 21:4 (1954), 587–591
- G. H. Hardy, J. E. Littlewood, “Some properties of fractional integrals. I”, Math. Z., 27:1 (1928), 565–606
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