电邮这篇文章 Recovery of integrable functions and trigonometric series
- 作者: Plotnikov M.G.1,2,3
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隶属关系:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Vologda State University
- 期: 卷 212, 编号 6 (2021)
- 页面: 109-125
- 栏目: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/142344
- DOI: https://doi.org/10.4213/sm9459
- ID: 142344
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详细
Classes $\Gamma$ of $L_1$-functions with fixed rate of decrease of their Fourier coefficients are considered. For each class $\Gamma$, it is shown that there exists a (recovery) set $G$ with arbitrarily small measure such that any function in $\Gamma$ can be recovered from its values on $G$. A formula for evaluation of the Fourier coefficients of such a function from its values on $G$ is given. In addition, it is shown that, for any $L_1$-function, a function-specific recovery set can be found. The problem of recovery of general trigonometric series from the Zygmund classes which converge to summable functions on such sets $G$ is also solved. Bibliography: 10 titles.
作者简介
Mikhail Plotnikov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics; Vologda State University
Email: mgplotnikov@gmail.com
Doctor of physico-mathematical sciences, no status
参考
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- С. А. Смоляк, Об оптимальном восстановлении функций и функционалов от них, Дисс. … канд. физ.-матем. наук, МГУ, М., 1965
- V. F. Babenko, V. V. Babenko, M. V. Polischuk, On optimal recovery of integrals of set-valued functions
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- J.-P. Kahane, Y. Katznelson, “Sur les ensembles d'unicite $U(varepsilon)$ de Zygmund”, C. R. Acad. Sci. Paris Ser. A-B, 277 (1973), A893–A895
- Н. К. Бари, Тригонометрические ряды, Физматгиз, М., 1961, 936 с.
- И. П. Натансон, Теория функций вещественной переменной, 3-е изд., испр., Лань, СПб., 1999, 560 с.
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