Email this article Recovery of integrable functions and trigonometric series
- Authors: Plotnikov M.G.1,2,3
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Vologda State University
- Issue: Vol 212, No 6 (2021)
- Pages: 109-125
- Section: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/142344
- DOI: https://doi.org/10.4213/sm9459
- ID: 142344
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Abstract
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.
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About the authors
Mikhail Gennadevich 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
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