Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivativesстатья
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Дата последнего поиска статьи во внешних источниках: 21 апреля 2014 г.
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.