Мақаланы E-mail арқылы жіберу Recovery of integrable functions and trigonometric series
- Авторлар: Plotnikov M.G.1,2,3
-
Мекемелер:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Vologda State University
- Шығарылым: Том 212, № 6 (2021)
- Беттер: 109-125
- Бөлім: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/142344
- DOI: https://doi.org/10.4213/sm9459
- ID: 142344
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
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.
Негізгі сөздер
Авторлар туралы
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
Әдебиет тізімі
- Б. Д. Боянов, “Оптимальные квадратурные формулы”, УМН, 60:6(366) (2005), 33–52
- 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
- V. N. Temlyakov, “The Marcinkiewicz-type discretization theorems”, Constr. Approx., 48:2 (2018), 337–369
- И. Добеши, Десять лекций по вейвлетам, НИЦ “Регулярная и хаотическая динамика”, М.–Ижевск, 2001, 464 с.
- A. S. Kechris, A. Louveau, Descriptive set theory and the structure of sets of uniqueness, London Math. Soc. Lecture Note Ser., 128, Cambridge Univ. Press, Cambridge, 1987, viii+367 pp.
- А. Зигмунд, Тригонометрические ряды, т. 1, Мир, М., 1965, 615 с.
- 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.
Қосымша файлдар
