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Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivativesстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 21 апреля 2014 г.
- Авторы: Magaril-Il'yaev G.G., Osipenko K.Yu
- Журнал: Functional Analysis and its Applications
- Том: 37
- Номер: 3
- Год издания: 2003
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 203
- Последняя страница: 214
- DOI: 10.1023/A:1026084617039
- Аннотация: We study problems of optimal recovery of functions and their derivatives in the L 2 metric on the line from information about the Fourier transform of the function in question known approximately on a finite interval or on the entire line. Exact values of optimal recovery errors and closed-form expressions for optimal recovery methods are obtained. We also prove a sharp inequality for derivatives (closely related to these recovery problems), which estimates the kth derivative of a function in the L 2-norm on the line via the L 2-norm of the nth derivative and the L p-norm of the Fourier transform of the function.
- Добавил в систему: Магарил-Ильяев Георгий Георгиевич