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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 3, Pages 51–64
DOI: https://doi.org/10.4213/faa157 (Mi faa157) 		 
This article is cited in 56 scientific papers (total in 56 papers)

Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives

G. G. Magaril-Il'yaeva, K. Yu. Osipenkob

a Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
b Moscow Aviation Technological Institute
Full-text PDF (180 kB) Citations (56)
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DOI: https://doi.org/10.4213/faa157
Abstract: 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 $k$th derivative of a function in the $L_2$-norm on the line via the $L_2$-norm of the $n$th derivative and the $L_p$-norm of the Fourier transform of the function.
Keywords: optimal recovery, Fourier transform, inequality for derivatives.
Received: 22.07.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 3, Pages 203–214
DOI: https://doi.org/10.1023/A:1026084617039
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives”, Funktsional. Anal. i Prilozhen., 37:3 (2003), 51–64; Funct. Anal. Appl., 37:3 (2003), 203–214
Citation in format AMSBIB
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    • This publication is cited in the following 56 articles:
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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